To complete the perfect trinomial, we add (5/2)² to the given equation and get:
[tex]x^2+5x+(\frac{5}{2})^2+6=(\frac{5}{2})^2.[/tex]Subtracting 6 we get:
[tex]x^2+5x+(\frac{5}{2})^2=\frac{25}{4}-6=\frac{1}{4}.[/tex]Therefore:
[tex](x+\frac{5}{2})^2=\frac{1}{4}.[/tex]Finally, we get:
[tex]\begin{gathered} x+\frac{5}{2}=\pm\sqrt{\frac{1}{4}}, \\ x=\pm\frac{1}{2}-\frac{5}{2}. \end{gathered}[/tex]Answer: [tex]\begin{gathered} x_=-3,\text{ or x=-2.} \\ \end{gathered}[/tex]write 1.09 × 10^-4 in standard notation
1.09 × 10^-4 in standard form is
[tex]\text{ 1.09 x 10}^{-4}[/tex]please help me ASAP!!
We have to solve:
[tex]\begin{gathered} 2^x-3=(x-6)^2-4_{} \\ 2^x-3+4=(x-6)^2 \\ 2^x+1=(x-6)^2 \end{gathered}[/tex]We can not write a explicit expression to find the value of x, but we can test each option to see which one is correct:
[tex]\begin{gathered} x=5 \\ 2^5+1=(5-6)^2 \\ 33=(-1)^2\longrightarrow\text{Not true} \end{gathered}[/tex][tex]\begin{gathered} x=3 \\ 2^3+1=(3-6)^2 \\ 8+1=(-3)^2 \\ 9=9\longrightarrow\text{True} \end{gathered}[/tex][tex]\begin{gathered} x=4 \\ 2^4+1=(4-6)^2 \\ 17=(-2)^2\longrightarrow\text{Not true} \end{gathered}[/tex][tex]\begin{gathered} x=-2 \\ 2^{-2}+1=(-2-6)^2 \\ \frac{1}{4}+1=(-8)^2\longrightarrow\text{Not true} \end{gathered}[/tex]Answer: x=3
Question 4 2 pts A fireman leaned a 36-foot ladder against a building. If he placed the ladder 12 feet from the base of the building, what angle is formed between the ladder and the ground? 0 78.8 Degrees 70.5 Degrees O 77.2 Degrees O 80.4 Degrees O 75.5 Degrees « Previous
x is the ladder ,x =36
y is the distance between ladder and wall y=12
z is the wall
we have in this triangle , only the hypotenuse(x) and the adjacent side
so,'
[tex]\cos \theta=\frac{y}{x}=\frac{12}{36}=0.33[/tex][tex]\theta=\cos ^{-1}(0.33)[/tex][tex]\theta=70\circ(approximately)[/tex]I need help with this worksheet that’s due tomorrow for algebra 1 it’s about Characteristics of Quadratic Functions
We have the following quadratic Function in a graph:
Now, we solve one aspect at a time:
Zeros
Let's remember that the zeros or roots of the quadratic function are those values of x for which the expression is 0. Graphically, the roots correspond to the abscissae of the points where the parabola intersects the x-axis.
By looking at the graph we can identify these, which in this case it is:
[tex](-2,0)[/tex]Axis of symmetry
Recall that the graph of a quadratic function is a parabola. The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves. The axis of symmetry always passes through the vertex of the parabola.
By looking at the graph we can identify this, which in this case it is:
[tex]x=-2[/tex]Max or min
In mathematical analysis, the maxima and minima of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range or on the entire domain.
By looking at the graph we can identify this, which in this case it is:
[tex]y=0[/tex]Vertex
Remember that the vertex of a quadratic equation or parabola is the highest or lowest point of the graph corresponding to that function. The vertex lies in the plane of symmetry of the parabola; whatever happens to the left of this point will be an exact reflection of what happens to the right.
By looking at the graph we can identify this, which in this case it is:
[tex](-2,0)[/tex]How to make 9/2=x/24 a equation
Answer:
I wasn't too sure of your question, but this is what made sense to me.
Step-by-step explanation:
cross multiplication seems to be the best fit for this.
Like this:
[tex]\frac{9}{2}=\frac{x}{24}\\ 2(x)=9(24)\\ 2x=216\\x= \frac{216}{2}\\ x=108[/tex]
Hope this helped in any way.
HELP ME ASAPPP
Mr. Anderson worked with the following number of students each year.
42 in 2023-2024
256 in 2022-2023
195 in 2021-2022
228 in 2020-2021
174 in 2019-2020
136 in 2018-2019
216 in 2017-2018
204 in 2016-2017
151 in 2015-2016
What would we call 42 in this situation?
A.
Mean Absolute Deviation
B.
Mode
C.
Outlier
D.
Range
what is the answer to 389+_=2,897
Answer:
the answer is 2508
a) Rotation, then reflectionb) Reflection, then rotation c) Reflection, then translationd) Rotation, then translation
The first transformation applied to the pre image is a reflection.
The second transformation applied is a 270° rotation.
It means the right answer is Reflection, then rotation.
Part A and B answer snd explaintion please
Answer:
Step-by-step explanation:
63 and 117
Margaret can fit 17 pencils in a small box and 50 pencils in a large box. She has 10 small boxes of pencils and would like to reorganize the pencils into large boxes. How many large boxes could she fill?
Answer:
She can fill five boxes with 20 pencils left over.
Step-by-step explanation:
17x10=170
170/50=3.4
50x3=150
170-150=20
Elena is making an open top box by cutting squares out of the corners of a piece of paper that is 11 inches wide and 17 in long and then folding up the sides if the side length of a square cut outs RX in in the volume of the box is given by [tex]v(x) = x(11 - 2x)(17 - 2x)[/tex]what is a reasonable domain for V of x?approximately which value of x will give her a box with the greatest volume round to the nearest whole numberfor approximately which values of X is the volume of the Box increasing round to the nearest whole number
The expression for the volume of the box is:
[tex]v(x)=x(11-2x)(17-2x)[/tex]Mathematically, there is no restriction for the values of x, but phisically we know that x is a length and has a positive value, so x>0.
Also, we know that x can not be largest than half of the width, that is the smallest dimension of the piece of paper.
As the width is 11, we then know that x is smaller than 11/2=5.5.
In conclusion, the domain for x is:
[tex]0To calculate the maximum volume for the box we have to derive the volume function and equal to zero:[tex]\begin{gathered} v(x)=x(11-2x)(17-2x) \\ v(x)=x(11\cdot17-11\cdot2x-2x\cdot17+4x^2) \\ v(x)=x(4x^2-56x+187) \\ v(x)=4x^3-56x^2+187x \end{gathered}[/tex][tex]\begin{gathered} \frac{dv}{dx}=4(3x^2)-56(2x)+187(1)=0 \\ 12x^2-112x+187=0 \\ x=\frac{-(-112)\pm\sqrt[]{(-112)^2-4\cdot12\cdot187}}{2\cdot12} \\ x=\frac{112\pm\sqrt[]{12544-8976}}{24} \\ x=\frac{112\pm\sqrt[]{3568}}{24} \\ x=\frac{112}{24}\pm\frac{59.73}{24} \\ x=4.67\pm2.49 \\ x_1=4.67-2.49=2.18\approx2 \\ x_2=4.67+2.49=7.16\approx7 \end{gathered}[/tex]The solutions are x=2 and x=7 approximately.
Because of our domain definition, we know that x=7 is not a valid solution, so the value of x that maximizes the volume is x=2.
The volume for x=0 is 0. Then, it will increase its value until x=2, where it reaches the maximum volume. From x=2 to x=5.5, the volume decrease until reaching v=0 at x=6.5.
Answer:
Domain: 0
Value of x that maximizes the volume: x=2.
From x=0 to x=2 the volume of the box increases.
I need the answers as soon as you can! I’m on the clock
1) The first thing to do is to find the vertex. So let's do it, considering that we already have the vertex and then we can find the coefficients. Note that all functions have a=1:
[tex]\begin{gathered} h=-\frac{b}{2a} \\ 9=\frac{-b}{2(-1)} \\ 9\cdot-2=-b \\ -b=-18 \\ b=18 \\ ----- \\ \end{gathered}[/tex]2) Now, let's find the other coefficient "c", since we've got a,b.
[tex]\begin{gathered} k=\frac{-\Delta}{4a} \\ 7=\frac{-(18^2-4(-1)(c))}{4(1)} \\ 28=-(324+4c) \\ 28=-324-4c \\ 28+324=-4c \\ 352=-4c \\ c=\frac{352}{-4} \\ c=-88 \end{gathered}[/tex]3) Thus the answer is:
[tex]D[/tex]A flower bed is in the shape of a triangle with one side twice the length of the shortest side and the third
side is 13 feet more than the length of the shortest side. Find the dimensions if the perimeter is 157 feet.
Answer:
The triangle has sides of 36 feet, 72 feet, and 49 feet.
=====================================================
x = shortest side
2x = second side
x+13 = third side
The three sides add up to the perimeter of 157
(x)+(2x)+(x+13) = 157
4x+13 = 157
4x = 157-13
4x = 144
x = 144/4
x = 36
The shortest side is 36 feet.
The second side is 2x = 2*36 = 72 feet.
The third side is x+13 = 36+13 = 49 feet.
Check:
side1+side2+side3 = 36+72+49 = 157
The answers are confirmed.
please helpjjjjjjjjjjjjjjjj
Answer:
Diverge i think.
Step-by-step explanation:
See the photo
In triangle ABC, the segments drawn from the vertices intersect at point G. Segment FG measures 6 cm, and segment FC measures 18 cm. Which best explains whether point G can be the centroid? (are the answers given here right? cos I'm not quite sure)
A centroid divides each median in a ratio 2:1, in this case, the segment FC is the sum of the segments FG and GC:
[tex]FC=FG+GC[/tex]By solving for GC, we get:
[tex]GC=FC-FG=18-6=12[/tex]Then, the part of the median that goes from C to G has a length of 12 and the part that goes from the centroid to F has a length of 6, then we can express their ratio as 12:6, which is equivalent to 2:1.
Then the answer is:
Point G can be the centroid because 12:6 equals 2:1
f(x)=[tex]\sqrt{x}[/tex], g(x)=x+9
A: (fg)(x)= ??, Domaine of fg=?
B(gf)(x)=??, Domaine of gf=?
The values are as:
a) f(g(x)) = √(x+ 9)
b) (gf)(x)= √x +9
What is function?The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The whole set of values that the function's output can produce is referred to as the range. The set of values that might be a function's outputs is known as the co-domain.
Given:
f(x)=√x, g(x)=x+9
a) (fg)(x)=
f(g(x)) = f( x+9)
= √(x+ 9)
Now, domain is all the input values
i.e., x=2, 4, 7
f(g(2)) = √(2+ 9)
= √11
and, f(g(4)) = √(4+ 9)
= √13
and, f(g(7)) = √(7 + 9)
= √16
= 4
b) (gf)(x)= g(f(x))
= g(√x)
= √x +9
Now, domain is all the input values
i.e., x=2, 4, 7
f(g(2)) = √2+ 9
and, f(g(4)) = √(4+ 9)
= 2+9
= 11
and, f(g(7)) = √7 + 9
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What property is being used here?
4x-3
x=2
4(2)-3
THE PROPERTY OF SUBSTITUTION IS USED. IF x=2 IT MEANS IN THE PLACE OF X IN THE EXPRESSION 4X-3 YOU WILL PLUG IN THE VALUE 2 AND SIMPLIFY.
[tex] = 4(2) - 3 \\ = 8 - 3 \\ = 5[/tex]
JUST AS I HAVE DONE ABOVE.
HOPE THIS HELPS
28282838383833883+182827272727277227
Answer:
[tex]211,110,111,111,111,110[/tex]Explanation:
We want to find the sum of the numbers;
[tex]28282838383833883+182827272727277227[/tex]solving;
Therefore;
[tex]28,282,838,383,833,883+182,827,272,727,277,227=211,110,111,111,111,110[/tex]Jackson puts 600.00 into an account to use for school expenses the account earns 2% interest compounded quarterly monthly how much will be in the account after 10 years round your answer to the nearest cent
By the compound interest formula, you know that
[tex]undefined[/tex]What is the answer to this?
Answer: 4/7
Step-by-step explanation:
There are 7 students with brothers, 4 of which have sisters.
So, the probability is 4/7.
The graph shows a coordinate plane that goes from negative 8 to 8 in each direction. The graph also shows two lines that intersect at ( 2 , 3 ). That point is labeled "solution." That's right. When you have two or more linear equations, it is called a "system of linear equations". The solution to a system of linear equations consists of the - and -value that make BOTH equations true. Graphically, this appears as the point where the lines intersect. In this case, the solution is the ordered pair , as shown on the graph. If you are trying to decide whether a system of equations has a solution, would you rather have the equations or the graphs? Why?
To visualize the solution of a system of equations, a graph is ideal, as we can see whether the functions intersect or not.
What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the context of the problem. The pair/tuple/... containing these values is called the solution of the system.
The equations that construct a system are functions, and the solution of a system is at the point of intersection of these functions. The intersection of two points is easier to visualize graphically then calculating, hence a graph is ideal, as we can see whether the functions intersect or not, while for the function we would have to calculate.
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The earth's average distance from the sun is 92,960,000 miles. Venus’s distance from the sun is an average of 67,230,000 miles. The Earth is how much farther from the sun than Venus? Express the answer in scientific notation.
Answer:
[tex]2.573 \times 10^7[/tex]
Step-by-step explanation:
[tex]92960000-67230000=25730000=2.573 \times 10^7[/tex]
Graph the linear function f(x)=4x+1 by plotting points.
To plot points, click on a point on the graph and drag it to the desired location.
A graph of the linear function (f(x) = 4x + 1) is shown in the image attached below.
What is a graph?A graph is a type of chart that's commonly used for the graphical representation of data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
Generally speaking, the graph of any proportional relationship such as a linear function is characterized by a straight line with the points passing through the origin (0, 0) because as the values on the x-axis increases or decreases, the values on the y-axis increases or decreases simultaneously as shown in the image attached below.
In conclusion, a graph which represents the given linear function shows a proportional relationship between the value of x and y.
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The mathematics section of a standardized college entrance exam had a mean of and an SD of for a recent year. Assume these are well modeled by a Normal distribution.
Normal distributions are crucial to statistics because they are widely used in the natural and social sciences to represent real-valued random variables whose distributions are unknown.
Normal distribution is a type of continuous probability distribution for a random variable with a real value.
They are important in part because of the central limit theorem. This claim asserts that, in some cases, the mean of many samples (observations) of a random variable with finite mean and variance is itself a random variable, whose distribution tends to converge to a normal distribution as the number of samples increases. Because of this, the distributions of physical quantities, such as measurement errors, which are assumed to represent the sum of multiple distinct processes, are usually close to normal. It may also be referred to as a Laplace-Gauss, Gaussian, or Gaussian distribution.[tex]{\displaystyle f(x)={\frac {1}{\sigma {\sqrt {2\pi }}}}e^{-{\frac {1}{2}}\left({\frac {x-\mu }{\sigma }}\right)^{2}}}[/tex]Another name for a normal distribution is a bell curve.The Cauchy, Student's t, and logistic distributions, among many others, have a bell-shaped structure.The univariate probability distribution is generalized for vectors in the multivariate normal distribution and for matrices in the matrix normal distribution.Hence we can use the normal distribution to find the mean and standard deviation of a data set.
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What is the solution and working?
The value of the length AB xcm = -3½ which is derived using the completing the square method, and satisfies the expression 2x² - 5x - 42 = 0.
Completing the square methodTo solve for the unknown value of a quadratic equation; say ax² + bx + c = 0:
First make the coefficient of x² one by dividing through by "a"Move the constant "c" to the right hand side of the equationDivide the coefficient of "x" by 2, square the result and add to both sides of the equation.The left hand side of the equation would have a complete square which will then be easier to solve for the value "x".From the derived quadratic equation, applying the method of completing the square as follows;
2x² - 5x - 42 = 0
divide through by 2
x² - (5/2)x - 21 = 0
add 21 to both sides
x² - (5/2)x = 21
divide the coefficient of x, square the result and add it to both sides
x² - (5/2)x + (5/4)(5/4) = 21 + (5/4)(5/4)
factor the left hand side of the equation
(x - 5/4)² = 21 + (25/16)
simplify the right hand side
(x - 5/4)² = 361/16
take the square root of both sides
x - 5/4 = (+ or -)(19/4)
then;
x = 5/4 + 19/4 or 5/4 - 19/4
x = 3 or x = -3½
The quadratic equation 2x² - 5x - 42 = 0 is true for the value of x = -3½.
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MATH HELP PLEASEEEE 35 POINTS
Answer:
Step-by-step explanation:
3.75 is a2 x (b-c)
4.85 gose with the b + c -a
3.3 gose to the a - b + c
you should now know the last one
Answer:
1. A² × ( B - C ) = 3.75
2. B + C - A = 3.65
3. A - B + C = 4.85
4. B × ( A - C ) = 3.3
Step-by-step explanation:
1. (5 × 5) × (4.4 - 4.25)
25 × .15 = 3.75
2. (4.4 + 4.25) - 5
8.65 - 5 = 3.65
3. (5 - 4.4) + 4.25
.6 + 4.25 = 4.85
4. 4.4 × ( 5 - 4.25 )
4.4 × .75 = 3.3
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Given f(x) = 2x² + 2x + k, and the remainder when f(x) is divided by x - 1 is
13, then what is the value of k?
Answer:
Step-by-step explanation:
Set up either long division or synthetic div. I'd do the latter.
Your divisor for synth. div. should be -7.
__________
Then -7 / 2 9 k
-14 +35
--------------------
2 -5 k+35 Rem is 32;
Let 32 = k + 5 and solve for k:
k = -3.
Let's check that. Is k correct?
Then -7 / 2 9 -3
-14 +35
--------------------
2 -5 -3+35 = 32
Since the rem is 32, we are correct; k = -3.
Ricky grows plants for a science project at the start of his project the plants average a height of 3 inches after three weeks the average player height was 7 inches what was the percent of the change in the average height of the plants?
To answer this question, we will use the following formula for the percent of change:
[tex]P=\frac{F-I}{I}\times100,[/tex]where F is the final height and I is the initial height.
Substituting F=7, and I=3 we get:
[tex]P=\frac{7-3}{3}\times100.[/tex]Simplifying the above result we get:
[tex]F=\frac{400}{3}\text{.}[/tex]Answer: 400/3 %.
Lesson 2: Exit Ticket
Flipping Ferraris
Find the inverse of each function:
b. g(x)= √x
The inverse of the functions given as y = 5(x-2) and f^-1(x) = x²
Inverse of a functionA function's inverse function reverses the action of a function, or f.
a) From the given table, we can use the coordinate points (-5, 1) and (0, 2)
The standard linear equation is y = mx + b
m = 2-1/0-(-5)
m = 1/5
Since the y-intercept is (0, 2), hence the required function is y = 1/5 x + 2.
y = 1/5x + 2
x = 1/5 y + 2
1/5 y = x - 2
y = 5(x-2)
b) For the function g(x) = √x
y = √x
x = √y
y = x²
f^-1(x) = x²
This gives the inverse of the function.
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Find the area of the shaded region show or explain your reasoning
The area of the shaded region will be 28 cm². The shaded region is a combination of two rectangles.
What is the area of the shaded region?The area of the shaded area is the difference between the total area of the polygon and the area of the portion of the polygon that is not shaded. In polygons, the area of the shaded component might appear in two different ways. A polygon's sides or its center are both potential locations for the shaded area.
From the triangle, it is obtained that the shaded region is the combination of a 4×6 rectangle and a 2×2 square.
Area of shaded region = Area of rectangle + Area of square
Area of shaded region = (6-2)×6 + 2×2
Area of shaded region = 4×6 + 4
Area of shaded region = 24 + 4
Area of shaded region = = 28 cm²
Thus, the area of the shaded region will be 28 cm². The shaded region is a combination of two rectangles.
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