Answers
SOLUTION
The given equation is:
[tex]g(x)=13+x^2-6x[/tex]Rewrite the equation in general form:
[tex]g(x)=x^2-6x+13[/tex]The standard form of a quadratic function is of the form:
[tex]g(x)=a(x-h)+k[/tex]Rewriting g(x) in standard form is done as follows:
[tex]\begin{gathered} g(x)=x^{2}-6x+13 \\ g(x)=x^2-6x+3^2+4 \\ g(x)=(x-3)^2+4 \end{gathered}[/tex]Therefore the standard form of the given function is:
[tex]g\mleft(x\mright)=\left(x-3\right)^2+4[/tex]Related Questions
Jalme drew a snowflake on graph paper. What is its area in square unit? Show your work
Answers
We can divide the snowflake into a big square and a 2 small squares as:
The big square has side c with measure
[tex]3^2+3^2=c^2[/tex]which was obtained from the following right triangle:
Then, c (the lenght of the square sides) is given by
[tex]\begin{gathered} c=\sqrt[]{3^2+3^2} \\ c=\sqrt[]{9+9} \\ c=\sqrt[]{2\cdot9} \\ c=3\sqrt[]{2} \end{gathered}[/tex]Therefore, the area of the big square is
[tex]\begin{gathered} A_{\text{Big}}=c^2 \\ A_{\text{Big}}=(3\sqrt[]{2})^2 \\ A_{\text{Big}}=9\cdot2 \\ A_{\text{Big}}=18units^2 \end{gathered}[/tex]Now, the sides of the small squares measure 1 unit, then the area of one small square is
[tex]\begin{gathered} A_{\text{small}}=1^2 \\ A_{\text{small}}=1units^2 \end{gathered}[/tex]Finally, the total area is
[tex]A=A_{\text{big}}+4\cdot A_{\text{small}}[/tex]By substituting the last results, we get
[tex]\begin{gathered} A=18+4\cdot1 \\ A=18+4 \\ A=22units^2 \end{gathered}[/tex]that is, the area of the snowflake is 22 units^2.
Find the midpoint of AB. A is at (7,-8) and B is at (-3, 6).
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The midpoint is the average of the x coordinates and the average of the y coordinates given.
Given the 2 pair of points:
A = (7, - 8)
B = (-3, 6)
Let the midpoint have coordinates (x, y).
To find x, we take the average of x-coordinates of A and B, shown below.
[tex]\begin{gathered} x=\frac{7-3}{2} \\ x=\frac{4}{2} \\ x=2 \end{gathered}[/tex]To find y, we take the average of y-coordinates of A and B, shown below.
[tex]\begin{gathered} y=\frac{-8+6}{2} \\ y=-\frac{2}{2} \\ y=-1 \end{gathered}[/tex]The midpoint is (2, -1)find the zeros of the function f( x) equals x squared plus 2X minus 3
Answers
f(x) =x² + 2x - 3
The zeros of the function is the x-value for which the function equals to zero.
To find such x-value, simply substitute f(x) =0 and the solve forx
x² + 2x - 3 =0
We can solve using the factorization method
Find two numbers such that its product gives -3 and its sum gives 2.
The numbers are : +3 and -1
Replace the coefficient of x by the two numbers
x² + 3x - x - 3 = 0
x(x+ 3) - 1(x+3) = 0
(x+3)(x- 1) = 0
x+3 = 0 and x- 1 = 0
x = -3 and x= 1
Therefore, the zeros of the functions are: D)(-3,0) and (1,0)
Find the volume of the following figure.1.5m2.5 m6 m
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Start by dividing the figure into 2 prisms
calculate the volume for both independently.
For the rectangular prism
[tex]V=l\cdot w\cdot h[/tex]then,
[tex]\begin{gathered} V=2\cdot2.5\cdot1.5 \\ V=7.5m^3 \end{gathered}[/tex]For the triangular prism
[tex]V=\frac{1}{2}l\cdot h\cdot w[/tex]then,
[tex]\begin{gathered} V=\frac{1}{2}\cdot1.5\cdot4\cdot2.5 \\ V=7.5m^3 \end{gathered}[/tex]Add both volumes together
[tex]\begin{gathered} V_t=7.5m^3+7.5m^3 \\ V_t=15m^3 \end{gathered}[/tex]Which point would map onto itself after a reflection across the line y = -x? (-4, 4) (-4, 0) (0, -4) (4,4)
Answers
Answer:
The point that would map onto itself after a reflection across the line is (-4, 0)
Explanation:
Given the points:
(-4, 4), (-4, 0), (0, -4) and (4, 4)
The point that would map onto itself after a reflection across the line:
y = -x
is (-4, 0)
because it is the point in the line y = -x
Put these points into an equation IN STANDARD FORM!!!!!!
(3,0) and (0,-7)
Answers
⇒The standard form of a straight line equation is given by y= mx+c
where m is the gradient and (x, y) are the given points and c is the y intercept.
⇒We can the gradient of the line using the formula
⇒[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\\ m=\frac{-7-0}{0-3} \\m=\frac{-7}{-3}\\m=\frac{7}{3}[/tex]
⇒To find the value of c we can plug in any point in the equation y=mx+c ,you will get the same value.
⇒I will use the point (3,0)
[tex]0=\frac{7}{3}(3)+c\\ 0=7+c\\c=-7[/tex]
This simply means that the equation of the straight line is
[tex]y=\frac{7}{3} x-7[/tex]
GoodLuck!!
The equation in standard form for the line that passes through the given points (3,0) and (0, -7) will be 2x + 3y = 12.
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.
It is given that the line that passes through the given points (3,0) and (0, -7) is
The slope m of the line is,
m = (y₂-y₁) / (x₂ - x₁)
m =3 - 0 / 0 -7
m = 3 / -7
The standard equation of the line is,
y - y₁ = m(x - x₁)
y - 0 = -2/3 (x + 7)
y = -2/3x + 4
y+2/3x =4
Multiply by 3 in the whole equation,
3(2/3x + y = 4)
2x + 3y = 12
Thus, the equation in standard form for the line that passes through the given points (3,0) and (0, -7) will be 2x + 3y = 12.
Learn more about the linear equation at:
brainly.com/question/11897796
I need help to find the indicated operation:h(t)= 2t-1g(t)= t^3+2Find (h×g)(t)
Answers
(h o g)(t) is 2t^3+3.
Given:
[tex]\begin{gathered} h(t)=2t-1 \\ g(t)=t^3+2 \end{gathered}[/tex]The objective is to find composite functions, (h o g)(t).
The composite function can be calculated as,
[tex]\begin{gathered} (h\circ g)(t)=h(g(t)) \\ =h(t^3+2) \\ =2(t^3+2)-1 \\ =2t^3+2(2)-1 \\ =2t^3+4-1 \\ =2t^3+3 \end{gathered}[/tex]Hence, the composite functions, (h o g)(t) is 2t^3+3.
I need help finding 5 points. 2 to the left of the vertex, the vertex, and 2 to the right of the vertex. the graph only goes up to 14
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In order to graph the parabola, first let's identify the x-coordinate of the vertex.
To do so, we can use the formula below, after identifying the parameters a, b and c from the standard form of the equation:
[tex]\begin{gathered} x_v=\frac{-b}{2a} \\ \\ y=ax^2+bx+c \\ a=-3,b=0,c=3 \\ \\ x_v=\frac{-0}{2\cdot(-3)}=0 \end{gathered}[/tex]Now, let's calculate the points using x = -2, x = -1, x = 0, x = 1 and x = 2:
[tex]\begin{gathered} x=-2\colon \\ y=-3(-2)^2+3=-3\cdot4+3=-12+3=-9 \\ x=-1\colon \\ y=-3(-1)^2+3=-3\cdot1+3=0 \\ x=0\colon \\ y=-3\cdot0^2+3=0+3=3 \\ x=1\colon \\ y=-3\cdot1^2+3=0 \\ x=2\colon \\ y=-3\cdot2^2+3=-12+3=-9 \end{gathered}[/tex]Graphing these points and the corresponding parabola, we have:
Joe solved the equation 3 + = 10 and justified each step as shown.Identify Joe's error and fix his mistake.StepJustification3+ = 10Given equationX = 7Multiplication Property of EqualityX= 14Subtraction Property of EqualityAnswer:
Answers
The justification of the second and third step are wrong,
the justification he gave for the second step should be the justification of step 3. And the justification of step 3 should be the justification for step 2
Jessica gave 6 people candy. She split 7/8 pounds among them. What is the unit rate in pounds per person
Answers
Number of people: 6
Number of pounds: 7/8
The unit rate in pounds per person can be calculated using the formula:
[tex]\text{ unit rate }=\frac{\text{ number of pounds}}{\text{ number of people}}[/tex]Then, using the values from the beginning:
[tex]\begin{gathered} \text{ unit rate }=\frac{7/8}{6}=\frac{7}{8\cdot6} \\ \\ \therefore\text{ unit rate }=\frac{7}{48}\text{ pounds per person} \end{gathered}[/tex]
Mrs. Mazzucco dumps out her change purse and finds that
she has 15 coins, all dimes and quarters, for a total of $2.70.
How many quarters does she have?
Answers
Answer: 10 quarters and 2 dimes.
Step-by-step explanation:
4 quarters = 1 dollar
1 quarter = 25 cents
1 dime = 10 cents
If 4 quarters are 1 dollar then 2 dollars would be 8 quarters.
8 quarters + 2 quarters (50 cents) would be 2.50
You cant add another quarter or that would be 2.75.
Instead you do: 10 quarters + 2 dimes = 2.70
So to sum it all up there are 10 quarters and 2 dimes.
A rectangle is placed around a semi circle as shown below the length of the rectangle is 12mm. Find The area of the shaded region. Use the value 3.14 for pi, and do not round your answer be sure to include the correct unit in your answer.
Answers
Explanation
We are given a rectangle placed around a semi-circle as shw in the image below:
We are required to determine the area of the shaded portion.
This is achieved thus:
The area of the shaded portion is given as:
[tex]\begin{gathered} Area=Area\text{ }of\text{ }rectangle-Area\text{ }of\text{ }semicircle \\ Area=A_r-A_s \end{gathered}[/tex]The dimension of the rectangle is given as:
[tex]\begin{gathered} Length=Diameter\text{ }of\text{ }the\text{ }semicircle=12mm \\ Width=Radius\text{ }of\text{ }the\text{ }semicircle=\frac{12}{2}=6mm \end{gathered}[/tex]Therefore, the area of the shaded portion is:
[tex]\begin{gathered} Area=A_r-A_s \\ Area=(l\times w)-(\frac{\pi r^2}{2}) \\ Area=(12\times6)-(\frac{3.14\times6^2}{2}) \\ Area=(72)-(56.52) \\ Area=15.48mm^2 \end{gathered}[/tex]Hence, the answer is:
[tex]Area=15.48mm^{2}[/tex]You want to buy a car. The loan amount will be $35,000. The company is offering a 5% interest rate for 36 months (3years). What will your monthly payments be?
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Given that:
[tex]\begin{gathered} \text{Loan amount, P}_0=35000 \\ \text{Annual interst rate, r = }5\%=0.05 \\ \text{Number of compounding periods in one year, k =12} \\ L\text{ength of loan(in years), N = 3} \end{gathered}[/tex]Find the monthly payment, d.
The formula to find the monthly payment is
[tex]P_0=\frac{d(1-(1+\frac{r}{k})^{-Nk})}{(\frac{r}{k})}[/tex]Plug the given values into the formula.
[tex]\begin{gathered} 35000=\frac{d(1-(1+\frac{0.05}{12})^{-3\cdot12})}{(\frac{0.05}{12})} \\ =33.3657d \\ d=\frac{35000}{33.3657} \\ =1048.98 \end{gathered}[/tex]The monthly payment is $1049 approximately.
“ using the figure below, state 4 different angles that are congruent to EFC using 4 different conjectures. State the congruent angles and the appropriate conjecture” this is confusing if someone could help that would be appreciated
Answers
From the given figure
Since AC intersects EH at point F, then
Since AC // BD, and EH is the transversal
At Jebel Jais in UAE, there is a 40-mile mountain bike trail. Khaled rode ½ of the trail on Saturday and 1/9 of the trail on Sunday. He estimates that he rode more than 22 miles over the two days.What is the estimate of 1/2 + 1/9
Answers
The estimate of 1/2 + 1/9 is 24.444...
Explanation:Given that:
Khaled rode 1/2 of the trail on Saturday, and 1/9 of the trail on Sunday.
Since he estimated that he rode more than 22 miles over the two days.
1/2 of 40 = 1/2 * 40 = 20
1/9 of 40 = 1/9 * 40 = 4.4444...
His total ride was 24.4444...
Solve the inequalities|x| < 8
Answers
Given the following inequality:
[tex]|x|<8[/tex]According to the rules of the absolute values, the given inequality will be written as follows:
[tex]-8So, the answer will be:[tex]x=(-8,8)[/tex]The solution on the number line will be as follows:
The populations of two towns, town A and town B, are being compared. The population of town A is 8 x 104 and the population of B is 4 x 105 How many times greater is the population of town B than town A? A.5 B.50 C.500 D.5000
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The population of town A is 8 x 10^4
The population of town B is 4 x 10^5
it is required to find,
How many times greater is the population of town B than town A ?
So, divide the population of B by the population of A
So,
[tex]\frac{4\cdot10^5}{8\cdot10^4}=\frac{4\cdot10\cdot10^4}{8\cdot10^4}=\frac{4\cdot10}{8}=\frac{40}{8}=5[/tex]so, the answer is option A. 5
Directions: If each quadrilateral below is a parallelogram find the missing measures.
Answers
Given that CDEF is a parallelogram
So, every two opposite sides are equal in length
And the diagonals bisect each other
So, CD = FE , CF = DE , CG = EG and FG = DG
so,
[tex]\begin{gathered} CF=DE=10 \\ \\ FE=CD=15 \\ \\ CE=2\cdot CG=2\cdot7=14 \\ \\ GD=\frac{1}{2}FD=\frac{1}{2}\cdot22=11 \end{gathered}[/tex]
An extra-large rectangular chocolate bar is 4 inches longer than its width. If the perimeter ofthe bar is 16 inches, find the width of the chocolate bar. Round to one decimal place.
Answers
The perimeter of a rectangle is given by the formula
[tex]P=2L+2W[/tex]we have
P=16 in
L=W+4
substitute given values in the formula
[tex]\begin{gathered} 16=2(W+4)+2W \\ solve\text{ for W} \\ 16=2W+8+2W \\ 4W=16-8 \\ 4W=8 \\ W=2\text{ in} \end{gathered}[/tex]Find out the value of L
[tex]\begin{gathered} L=W+4 \\ L=2+4 \\ L=6\text{ in} \end{gathered}[/tex]The width is 2.0 inchesdraw a model to support your solution 3/5 thought of juice is poured equally into 6 glasses how much juice is in each glass.
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We have to divide 3/5 by 6. The picture above represents 3/5.
Drawing 5 vertical lines, we divide the whole block into 6 equal parts.
Now we have a total of 5*6 = 30 little squares. Dividing 3/5 into 6 equal parts we shade 3 out of 30 little squares. Then, 3/5 ÷ 6 = 3/30 = 1/10 (simplifying)
0 2 20) 5x - (x + 2) >-5(1 + x) + 3 섥놈 SXX2=55*3 x>0 4.x.-25-5x-2 Darsx-23-2 985-272 vhose 22) Name one particular solution to question #20.
Answers
5x - (x + 2) > -5(1 + x) + 3
Removing parentheses and distributing
5x - x - 2 > -5*1 + (-5)*x + 3
4x - 2 > -5 - 5x + 3
4x - 2 > -2 - 5x
5x is subtracting on the right, then it will add on the left
4x -2 + 5x > -2
9x - 2 > -2
2 is subtracting on the left, then it will add on the right
9x > -2 + 2
9x > 0
9 is multiplying on the left, then it will divide on the right
x > 0/9
x > 0
Every x greater than zero is a solution, like for example 1, 2, 10, etc.
40. Assume the lines that appear to be tangent are tangent. O is the center of the circle. Findthe value of xmZP-12c. 102d. 24a. 78b. 39
Answers
Answer
a. 78
Step-by-step explanation
Given that side PQ is tangent to circle O, then angle Q measures 90 degrees.
The addition of the three interior angles of a triangle is equal to 180 degrees. Applying this to triangle PQO, we get:
[tex]\begin{gathered} m\angle P+m\angle Q+m\angle O=180\degree \\ 12\degree+90\degree+x=180\operatorname{\degree} \\ x=180\operatorname{\degree}-12\degree-90\degree \\ x=78\operatorname{\degree} \end{gathered}[/tex]2) Choose the correct answer.There could besolutions to an inequality.infinitely manytwocommonthree
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Most of the time, an inequality has more than one or even infinity solutions.
For example the inequality
[tex]x>3[/tex]The value of x can be any number greater than 3 up to infinity.
So the correct answer would be infinitely many
find the measure of the two missing sides for each figure below leave answer and rationalized and simplified form
Answers
Let's begin by identifying key information given to us:
We have one known angle & one side
[tex]\begin{gathered} \theta=60^{\circ} \\ adjacent(a)=2\sqrt[]{6} \\ opposite(b)=\text{?} \\ hypotenuse(c)=\text{?} \end{gathered}[/tex]Based on the information we have been provided, we will solve for the missing sides using Trigonometric Ratio (SOHCAHTOA). This is shown below:
[tex]\begin{gathered} TOA\Rightarrow\tan \theta=\frac{opposite}{adjacent} \\ tan\theta=\frac{opposite}{adjacent} \\ tan60^{\circ}=\frac{opposite}{2\sqrt[]{6}} \\ But,tan60^{\circ}=\sqrt[]{3} \\ opposite=2\sqrt[]{6}\text{ x }\sqrt[]{3} \\ opposite=2\sqrt[]{18} \\ \\ CAH\Rightarrow cos\theta=\frac{adjacent}{hypotenuse} \\ cos\theta=\frac{adjacent}{hypotenuse} \\ cos60^{\circ}=\frac{2\sqrt[]{6}}{hypotenuse} \\ But,\cos 60^{\circ}=\frac{1}{2} \\ hypotenuse\text{ x }\cos 60^{\circ}=2\sqrt[]{6} \\ hypotenuse=\frac{2\sqrt[]{6}}{\frac{1}{2}} \\ hypotenuse=\frac{2\cdot2\sqrt[]{6}}{1}=4\sqrt[]{6} \\ hypotenuse=4\sqrt[]{6} \end{gathered}[/tex]Evaluate the expression.3 - 5(11 + 4) = 52 = 0
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Evaluate the value of expression.
[tex]\begin{gathered} \frac{3-5(11+4)}{5^2}=\frac{3-5\cdot15}{25} \\ =\frac{3-75}{25} \\ =-\frac{72}{25} \\ =-2.88 \end{gathered}[/tex]So answer is -2.88.
The University of Texas system consists of 9 campuses and has a budget of $2.4 billion in state funding. If the money were to be allocated equally based on total student enrollment, how much would be appropriated per student, rounded to the nearest cent?
Answers
Step 1:
Given data
Total number of campuses = 9
Total budget = $2.4 billion
Total students
= 33629 + 52359 + 8912 + 21493 + 23049 + 20353 + 5431 + 28923 + 7776
= 231925
Step 2
Convert $2.4 billion to cent, multiply $2.4 billion by 100.
[tex]2.4\text{ b}illion\text{ dollars = 2400000000 dollars = 240000000000 cent}[/tex]Step 3:
Divide the total budget in cent by total number of students
[tex]\begin{gathered} \text{Money appropriated per student = }\frac{240000000000}{231925} \\ =\text{ 1034817.29} \\ =\text{ 1034817 cent} \end{gathered}[/tex]Final answer
1034817 cent
21.A taxi charges a base fee of $3.00 and $0.15 for every mile of the ride. What would be thecost of a 3.4 mile ride?A $0.51B $3.51C $10.20D $10.35
Answers
Given:
Base Charge of the taxi = $3.00
Charge of the ride per mile = $0.15
The base fee here is constant, irrespective of the distance covered.
Therefore, the cost of a 3.4 mile ride will be:
[tex]\begin{gathered} (0.15\ast\text{ 3.4) }+\text{ \$3} \\ =0.51\text{+ \$3 = \$}3.51 \end{gathered}[/tex]Therefore, the cost of a 3.4 mile ride will be $3.51
ANSWER:
$3.51
Monique is paid an hourly rate of $17.63 for regular-time work. What will be her double-time hourly pay rate for overtime worK?
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Monique is paid an hourly rate of $17.63 for regular-time work. What will be her double-time hourly pay rate for overtime worK?
In this problem , multiply the hourly rate by 2
so
(17.63)*2=$35.26
therefore
the answer is
$35.26
Dora has to pick a number between 400 and 500 Dora is thinking of a number between 500 and 600. When she divides it by a 1 digit number it has a remainder of 4. What could be Dora’s number
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Given:
When Dora divides the number between 500 and 600 by a 1 digit number gives the remainder 4.
Let x be the one-digit number that divides the number between 500 and 600. It gives the remainder 4.
[tex]\begin{gathered} 500+(10\times n)+i \\ n=0,1,2,..\ldots\text{.}.9 \\ \text{For i=4,9} \end{gathered}[/tex]It gives the remainder 4.
Therefore,
[tex]\begin{gathered} 500+10n+4\text{ and 500+10n+9 divided by 5 will give the remainder 4} \\ n=0,1,2,\ldots9 \end{gathered}[/tex]Answer:
[tex]\begin{gathered} 504+10n \\ 509+10n \\ n=0,1,2,\ldots.9 \\ \text{Divided by 5} \end{gathered}[/tex]The graph of a cosine function shows a reflection over the x-axis, an amplitude of 5, a period of 6, and a phase shift of 0.25 to the right.Which is the equation of the function described?a. f(x)=−5cos(πx/3−1/4)b. f(x)=−5cos(πx/3 − π/12)c. f(x)=−5cos(3πx − 1/4)d. f(x)=−5cos(πx/3 − 4π/3)
Answers
Answer:
Given that:
The graph of a cosine function shows a reflection over the x-axis, an amplitude of 5, a period of 6, and a phase shift of 0.25 to the right.
To find the equation of the function described.
Explanation:
we have that,
General formula of cosine function is,
[tex]f(x)=a\cos(b(x+c))+k[/tex]where a is amplitude, b is period factor, c is shift (left/right) and k is shift (up/down)
From given,
a=5
b=2pi/6=pi/3
c=0.25
we get,
[tex]f(x)=-5\cos\frac{\pi}{3}(x-0.25)[/tex][tex]f(x)=-5\cos\frac{\pi}{3}(x-\frac{1}{4})[/tex][tex]f(x)=-5\cos(\frac{\pi}{3}x-\frac{\pi}{12})[/tex]Answer is: option:b
[tex]f(x)=-5\cos(\frac{\pi}{3}x-\frac{\pi}{12})[/tex]