Give the standard form of the given equation below. If it is a quadratic equation, then give the a, b, and c coefficients. 3x2-2x-5x(x-7)=(x-2)(x+4)+1
Answers
Answer:
[tex]\begin{gathered} -3x^2+31x+7=0 \\ a=-3 \\ b=31 \\ c=7 \end{gathered}[/tex]Step-by-step explanation:
The quadratic equation in standard form is represented by:
[tex]ax^2+bx+c=0[/tex]For the following equation;
[tex]\begin{gathered} 3x^2-2x-5x(x-7)=(x-2)(x+4)+1 \\ 3x^2-2x-5x^2+35x=x^2+4x-2x-8+1 \\ -2x^2-2x+35x=x^2+2x-7 \end{gathered}[/tex]Compute all the terms on the left side, equalizing 0:
[tex]\begin{gathered} -3x^2+31x+7=0 \\ \text{Then, the a,b and c coefficeints would be:} \\ a=-3 \\ b=31 \\ c=7 \end{gathered}[/tex]Related Questions
7/9 ÷ 3/9 = ????????
Answers
7/9 ÷ 3/9 =
= (7•9)/( 3•9)
= 63/27 = 7/3
Answer is 7/3
Consider the function f(x) = (x+4)(x+2), Dilate f(x) by x to create a new function of a higher degree,
a. Write the dilation of f(x) as g(x).
b. Sketch the graph of g(x).
c. identify the zeros of the graph of the function g(x)
Answers
The dilated function g(x) will be g(x) = x(x + 4)(x + 2). The zeroes of function g(x) = x(x + 4)(x + 2) will be x = 0, x = - 4, x = -2. The graph of the function g(x) is attached.
What is scale factor? How it is used in Dilating coordinates?Scale factor is used to compare 2 quantities, indicating by how much one quantity is greater than the other. It is denoted by K. Mathematically-
K = a/b.
If a coordinate point (x, y) is dilated by a scale factor of [k], then the coordinate point after dilation will be - (kx, ky).
Given is the function -
f(x) = (x+4)(x+2)
[A] -
For dilating the given f(x) by [x] times -
g(x) = [tex]x[/tex] f(x)
g(x) = x(x + 4)(x + 2)
Therefore, the dilated function g(x) will be -
g(x) = x(x + 4)(x + 2)
[B] -
The graph of the function g(x) is attached with the answer.
[C] -
The points where the graph of g(x) touches or cuts the x - axis, will represent the zeroes of the function g(x) = x(x + 4)(x + 2). It can be seen that the points are -
x = 0
x = - 4
x = - 2
The zeroes of function g(x) = x(x + 4)(x + 2) will be x = 0, x = - 4, x = -2.
Therefore, the dilated function g(x) will be g(x) = x(x + 4)(x + 2). The zeroes of function g(x) = x(x + 4)(x + 2) will be x = 0, x = - 4, x = -2. The graph of the function g(x) is attached.
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In triangle JKL, tan(b°) = 3/4 and sin(b°) = 3/5 If triangle JKL is dilated by a scale factor of 3, what is cos(bº)?
Answers
ANSWER
cos(bº) = 4/5
EXPLANATION
When a triangle is dilated, the resulting triangle is similar to the original triangle. Therefore, the interior angles of the dilated triangle are congruent to the interior angles of the original triangle. This means that cos(bº) is the same for both triangles.
Using the relationship between these three trigonometric ratios:
[tex]\tan (bº)=\frac{\sin (bº)}{\cos (bº)}[/tex]We can find the cosine:
[tex]\cos (bº)=\frac{\sin (bº)}{\tan (bº)}[/tex][tex]\cos (bº)=\frac{\frac{3}{5}}{\frac{3}{4}}=\frac{3}{5}\colon\frac{3}{4}=\frac{3}{5}\times\frac{4}{3}=\frac{4}{5}[/tex]Find the product and write your answer in proper scientific notation (4.5 x 10³)/(3 x 10⁶)
Answers
Answer:
[tex]1.5\times10^{-3}[/tex]Explanation:
Given the rational expression
[tex]\frac{4.5\times10^3}{3\times10^6}[/tex]We can rewrite the fraction as:
[tex]=\frac{4.5}{3}\times\frac{10^3}{10^6}[/tex]We then simplify and apply the division law of indices to obtain:
[tex]\begin{gathered} =1.5\times10^{3-6} \\ =1.5\times10^{-3} \end{gathered}[/tex]Note: When you have the same base of an exponent and the terms are being divided, we simply subtract the power of the numerator from that of the denominator.
A. F(x) = -x^7+4x^3-2x^2B. F(x)= x^9+12x^8+x^7C. F(x) =x^8+4x^4+20x^2D. F(x) = -x^6+x^3-x^2
Answers
answer:
A. F(x) = -x^7+4x^3-2x^2
Timothy Tools is a company that produces hand-crafted hammers and wrenches. The following equations can be used to determine how many hammers the company can produce each day if x people are making hammers
Answers
The domain of the function of the equation cannot include zero because h(0) is not real.
A scale used to weigh objects is analogous to an equation. When the two pans are filled to the same level with anything, the scale will balance and the weights will be considered to be equal (such as grain).
To keep the balance in check, whenever any grain is taken out of one of the balance's pans, an equal amount must be taken out of the other pan. In general, if the same operation is carried out on both sides of an equation, the equation remains in balance.Equations that involve one or more functions and their derivatives are known as differential equations. By locating a derivative-free formulation for the function, they can be resolved.The equation is given as [tex]h(x) = \sqrt{2x^2+5x+3}[/tex]
The equation at x=0 given
h(0) = √(0+0-3)
or, h(0) = √(-3) which is an imaginary number
Therefore for the equation the value of x at 0 is undefined.
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Find the area and perimeter of a rhombus with a diagonals 15 in and 20 in
Answers
Given data:
The diagonals of rhombus d1 = 15 in and d2 = 20 in
The area of the rhombus,
[tex]\begin{gathered} A=\frac{1}{2}\times d1\times d2 \\ A=\frac{1}{2}\times15\times20 \\ A=150\text{ inches sq.} \end{gathered}[/tex]Now, to find the perimeter of rhombus we first find the side of rhombus.
The diagonal of the rhombus is considered as diameter, so the radius will be
d1 = r1 = 7.5
d2 = r2 = 10
So, by using the pythagorean theorem we find the side of the rhombus
[tex]\begin{gathered} h^2=(7.5)^2+(10)^2 \\ h^2=56.25+100 \\ h^2=156.25 \\ h=12.5 \end{gathered}[/tex]The perimeter of the rhombus is,
[tex]\begin{gathered} P=4\times side \\ P=4\times12.5 \\ P=50\text{ inches} \end{gathered}[/tex]Thus, the area is 150 in. sq. and perimeter is 50 in.
What does n mean?????
Answers
a. Data values are 13.4, 16.3, 14.2 , 15.4 , 14.2 ,17.5
b. ∑x = 91
c. n = 6
What is mean and data values?Adding all numbers in the data and then dividing by the number of values is called mean. Median is defined as the middle value when a data set is in such a way that it goes from least to the greatest value. Whereas the number that occurs most often in a data set is mode. Sample size is represented by "n". Whereas, symbol Σ denotes the summation.
For the given mean,
The data values are 3.4, 16.3, 14.2 , 15.4 , 14.2 ,17.5
Summation, ∑x = 3.4+ 16.3+ 14.2 + 15.4 + 14.2 +17.5
= 91
n is the number of data that is 6.
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A car rental company offers two plans for renting a car.
Plan A: 35 dollars per day and 10 cents per mile
Plan B: 55 dollars per day with free unlimited mileage
How many miles would you need to drive in one day for plan B to save you money?
Answers
Answer:
Less than 200 miles, A is cheaper
At 200 miles, they are the same
Over 200 miles, B is less expensive
Step-by-step explanation:
?? i am not good at this please help me thanks
Answers
Answer:
If I am not mistake I am pretty sure its graph B.
Step-by-step explanation:
Help please. Catching up on missed work from being out due to medical issues. Thank you in advance!
Answers
Let B be the number of cups of boiling water that we should mix with I cups of ice to get 3 cups of 110°F water.
Therefore, we can set the following equation:
[tex]\begin{gathered} B+I=3, \\ 220B+32I=110\cdot3. \end{gathered}[/tex]Subtracting B from the first equation we get:
[tex]\begin{gathered} B+I-B=3-B, \\ I=3-B\text{.} \end{gathered}[/tex]Substituting the above equation in the second one we get:
[tex]220B+32(3-B)=330.[/tex]Simplifying the above result we get:
[tex]\begin{gathered} 220B+96-32B=330, \\ 188B+96=330. \end{gathered}[/tex]Subtracting 96 to the above equation we get:
[tex]\begin{gathered} 188B+96-96=330-96, \\ 188B=234. \end{gathered}[/tex]Dividing the above equation by 188 we get:
[tex]\begin{gathered} \frac{188B}{188}=\frac{234}{188}, \\ B\approx1.24. \end{gathered}[/tex]Substituting B=1.24 at I=3-B we get:
[tex]I=3-1.24=1.76.[/tex]Answer:
[tex]\begin{gathered} 1.26\text{ cups of boiling water.} \\ 1.74\text{ cups of ice.} \end{gathered}[/tex]A packing carton has a square bottom 18 inches by 18 inches. If the capacity of the carton is 3cubic feet, how deep is the carton?
Answers
The packing carton has a square bottom with measures 18in x 18in and has a volume of V=3ft³
The volume of cubic prims can be calculated by multiplying its width by its length and height:
So the formula to calculate the volume is
[tex]V=w\cdot l\cdot h[/tex]If we know the width, length, and volume we can determine the height. First, write the formula for h, that is, divide the volume by the width and height:
[tex]h=\frac{V}{wl}[/tex]The units of the width and length are in inches and the volume is in cubic feet, to determine the height of the box, all units must be the same. To make the calculations easier I will pass the units from inches to feet.
The unit rate between inches and feet is the following:
[tex]1^{\doubleprime}=\frac{1}{12}ft[/tex]To express 18 inches in feet you have to multiply them by 1/12
[tex]18\cdot\frac{1}{12}=1.5[/tex]This means that the width and length of the box measure 1.5ft
Now we can determine the height of the box as follows:
w=l=1.5ft
V=3ft³
[tex]\begin{gathered} h=\frac{V}{wl} \\ h=\frac{3}{1.5\cdot1.5} \\ h=\frac{4}{3}ft \end{gathered}[/tex]The height of the box is 3/4ft, if you multiply it by 12 you can express the measure in inches:
[tex]\frac{3}{4}\cdot12=9[/tex]The box has a deph of 9 inches.
9.2 x 108 is how many times the value of 2.3 x 10²?
A. 4 x 104
B. 4 x 106
C. 6.9 x 104
D. 6.9 x 106
Answers
Answer:
B. [tex]4*10^6[/tex]
Step-by-step explanation:
All you have to do is divide the first value by the second value to find the ratio between the two numbers.
The equation would look like this:
[tex]\frac{9.2*10^8}{2.3*10^2}[/tex] or [tex]\frac{920000000}{230}[/tex]
Solving this gives you [tex]4 * 10^6[/tex], or 4000000.
You can also figure this out without a calculator. Simply subtract the smaller power from the larger power to get your exponent.
Since this problem has [tex]10^8[/tex] and [tex]10^2[/tex], subtract 2 from 8 to get 6. This will be the exponent in your answer, ruling out answers A and C.
Then, just estimate 9.2/2.3. You can do 9/2 to get 4.5, which is closer to 4. Therefore, D is ruled out, so the answer must be B.
Hope this helps :)
What is the value of the function at x=−3? Responses y = 3 y, = 3 y = 0 y, = 0 y = 4 y, = 4 y=−3
Answers
The function has a value of y = 4 when x =-3
How to determine the value of the function?The graph that completes the question is added as an attachment
From the graph, we can see that:
The graph of the function is a linear function
This is so because the function is a straight line
Note that:
Linear equations are equations that have constant average rates of change.
On the straight line, we can see that
The value of the function when x = -3 is 4
This means that
y = 4
Hence, the value of the function at x = -3 is y = 4
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Find the turning point of y=h(x) if h(x)=f(-x)f(x)=x^2-4x+12
Answers
Given:
[tex]y=h(x)\text{ where }h(x)=f(-x)\text{ and }f(x)=x^2-4x+12.[/tex]Required:
We need to find the turning point of y=h(x).
Explanation:
Replace x =-x in the function f(x) to find h(x).
[tex]f(-x)=(-x)^2-4(-x)+12.[/tex][tex]f(-x)=x^2+4x+12.[/tex]Replace f(-x)=y in the equation.
[tex]y=x^2+4x+12.[/tex][tex]y=x^2+2\times2x+4+8.[/tex][tex]y=x^2+2\times2x+2^2+8.[/tex][tex]Use\text{ }(a^2+2ab+b^2)=(a+b)^2.[/tex][tex]y=(x+2)^2+8.[/tex]Which is of the form
[tex]y=a(x-h)^2+k.[/tex]where a=1, h=-2, and k=8.
The point (h,k)=(-2,8) is the turning point.
Final answer:
The turning point of y=h(x) is (-2,8).
100 POINTS ANSWER CORRECTLY PLS
Answers
Answer:
1.) y = -3/4x +2
2.) y = x - 4
3.) y = 2/3x - 4
4.) y = -1/2x + 5
5.) y = 8/3x +5
Step-by-step explanation:
1.)
Parallel means that the slopes will be the same.
So, m = -3/4
To find the equation, we must first use point-slope form.
[tex]y-y_{1} =m(x-x_{1} )[/tex]
y-(-1) = -3/4(x-4)
Now we clean this up and solve for y to get the answer in slope intercept form.
y+1= -3/4x + 3 => y = -3/4x +2
2.)
Perpendicular means that the slope is the negative reciprocal of the slope of the first line.
So, m = 1 as the negative reciprocal of -1 is +1.
Once again, we use point-slope form and the clean it up and solve for y to get the answer in slope-intercept form.
y - (-3) = 1(x-1) => y + 3 = x-1 => y = x - 4
3.)
Similar to the previous one, but with slope m = 2/3 (negative reciprocal)
y - (-4) = 2/3 (x - 0) => y + 4 = 2/3x => y = 2/3x - 4
4.)
Similar to the previous one, but with slope m = -1/2 (negative reciprocal)
y - 4 = -1/2(x-2) => y - 4 = -1/2x +1 => y = -1/2x + 5
5.)
Similar to the previous one, but with slope m = 8/3 (negative reciprocal)
y - (-3) = 8/3(x - (-3)) => y + 3 = 8/3x +8 => y = 8/3x +5
suppose that 18 inches of wire cost 72 cents. using the same rate how much in cents will 36 inches cost?
Answers
Mark made the following shape using two rectangles and one triangle. What is the area of the figure he made?
Answers
Answer:
44 square centimetres.
Explanation:
The shape consists of two rectangles and one triangle with the following dimensions:
• A rectangle (Rectangle 1) with dimensions of 4cm by 2cm.
,• A rectangle (Rectangle 2) with dimensions 6cm by 4cm.
,• A triangle with base 6cm and height of 4cm.
Thus, the area of the figure made will be:
[tex]\begin{gathered} \text{Area of figure=Area of rectangle 1+Area of rectangle }2+\text{Area of }\triangle \\ =(4\times2)+(6\times4)+(\frac{1}{2}\times6\times4) \\ =8+24+12 \\ =44\operatorname{cm}^2 \end{gathered}[/tex]The area of the figure is 44 square centimetres.
Lin is paid $90 for 5 hours of work. She used the following table tocalculate how much she would be paid at this rate for 8 hours of work.1. What is the meaning of the 18that appears in the table?IAmount earned($)Time worked(hours)9052. Explain how Lin used this table tosolve the problem3. At this rate, how much would Linbe paid for 3 hours of work? For21 hours of work?1811448
Answers
From the table :
Lin worked for 5 hours and earned 90$
LIn worked for 1 hour and earned 18$
Lin worked for 8 hour
so the earning is
[tex]8\times18=144[/tex]Lin worked for 8 hours so the earning is 144$
If lin works for 3 hours then the earning is
So the answer for 3 hours is 54$.
[tex]3\times18=54\text{ dollar}[/tex]If lin works for 21 hours then the earning is
[tex]21\times18=378\text{ dollar}[/tex]so the answer for 21 hours is 378$.
Four points W, X, Y, Z are chosen at random on the circumference of a circle. What is the probability that WX > YZ?
Answers
The probability to choose WX > YZ is 1/2.
What is mean by Probability?
The term probability refers to the likelihood of an event occurring.
Given that;
Four points W, X, Y, Z are chosen at random on the circumference of a circle.
Now,
By the four points W, X, Y, Z we make two line WX and YZ.
So, There are two relation between the line WX and YZ.
Thus, The probability to choose WX > YZ is;
Probability = Possible event / Total possibility
= 1/2
Therefore, The probability to choose WX > YZ is 1/2.
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Sorry if it's blurry but could you help me with this please :)
Answers
We have the following:
We can see in the figure that it up by two units and shift 5 units to the right.
Therefore, que the answer is thr first option
Are the triangles congruent using AAS?
True
False
Answers
Answer: True
Step-by-step explanation:
If you look both triangles have the same angles, so that means that they are congruent.
Which graph best represents the solution set for all possible combinations of x, the number of hours she worked at her 1st job, and y, the number of hours she worked at her second job, in one week?
Answers
The equation must be x + y < 48
Graph
Ganymede is one of Jupiter’s moons. It takes Ganymede 7 days, 3 hours, and 15 minutes to make one rotation around Jupiter. How many hours does it take Ganymede to complete a full rotation? Show your work using the correct conversion factors and make sure all conversion factors are labeled with appropriate units. You should have more than one conversion factor shown.
Answers
The number of hours it will take Ganymede to complete a full rotation is; 171.25 hours.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
The first step must be to convert days to hours. A day is equivalent to the 24 hours.
1 day = 24 hours
24 x 7 = 168 hours
The second step must be to convert minutes to hours,
60 minutes = 1 hour
15 / 60 = 0.25 hours
Now, add up all the converted hours together;
Total hours = 168 hours + 3 hours + 0.25 hours
Total hours = 171.25 hours
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Please explain this to me
Answers
If a perpendicular b and b parallel to c, then the value of x = 8
Here b and c are parallel lines
The parallel lines are two lines in the same plane that are at equal distance from each other and that do not intersect at any point
Then a is perpendicular to b
The perpendicular lines are the line that forms the angle of 90 degrees for both angles
Therefore the given angles are 90 degrees
9x+18 = 90
9x = 90-18
9x = 72
x = 72/9
x = 8
Hence, If a perpendicular b and b parallel to c, then the value of x = 8
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Jordan is constructing a aregular hexagon inscribed in a circle. He labels the points on the circle as shown
Answers
Given,
The diagram of the circle with the vertex of the hexgon.
Required
The measure of arc VX, angle ZXV.
As known that,
The measure of the circle is 360 degree.
The measure of arc VX is,
[tex]Arc\text{ VX = 60 degree.}[/tex]The measure of angle ZXV is,
[tex]\angle ZXV=60^{\circ}[/tex]The measure of arc WZ is 180 degree.
Answer:
VX=120
ZXV=60
WZ
Step-by-step explanation: YOUR WELCOME PUTAS
There area 17,60 gaffs in a mile . What is the number of yards in a mile rounded to the nearest hundred? 1- How many places are in this number?2- What are the places? 3- What place are you rounding to?4- What digit is in that place?5- What place is to the right of the place you are rounding to?6- What digit is in that place?Is this digit 5 or greater?7- What is the rule for digits 5 or greater? 8- Will you need to change the hundreds digit? If so, to what? 9- Which places will you change to 0s?10- What is the number of yards in a mile rounded to the nearest hundred?
Answers
itWe were given the following:
[tex]1760yard=1mi[/tex]1.
There are 4 places in this number
2.
1 thousand + 7 hundred + 6 tens + 0 units
3.
We are rounding to the hundreds place
4.
Seven (7)
5.
To the right, we have the ''tens''
6.
Six(6). Yes, the digit is 5 or greater
7.
Digits that are 5 or greater than are approximated to the next digit
8.
Yes. From 7 to 8
9.
The tens place will be changed to 0
10.
The number of yards in a mile rounded to the nearest hundred is:
[tex]\begin{gathered} 1,760yards=1mi \\ 1,760\approx1800 \\ =1,800yards(to\text{ the nearest hundred)} \end{gathered}[/tex]Find the particular antiderivative F(x) of f(x) = 18x - 13 that satisfies F(1) = 11.
Answers
To get the antiderivative of the function, we will integrate F(x), as follows:
[tex]\begin{gathered} \int (18x-13)dx=\int 18xdx-\int 13dx \\ =\frac{1}{2}(18x^2)-13x+C \\ =9x^2-13x+C \end{gathered}[/tex]Now, to get the particular antiderivative, we evaluate the antiderivative for x = 1, and it must be equal to 11. This can be shown as:
[tex]\begin{gathered} 9(1)^2-13(1)+C=11 \\ 9-13+C=11 \\ C=11+13-9 \\ C=24-9 \\ C=15 \end{gathered}[/tex]Hence, the particular antiderivative is
[tex]F(x)=9x^2-13x+15[/tex]what variable expression should you subtract from both sides of the equation so that you are left with no variables on the right hand side
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
What variable expression should you subtract from both sides of the equation so that you are left with no variables on the right-hand side?
The variable expression is: subtract 5x from both sides so that you are left with no variables on the right-hand side
[tex]\begin{gathered} 6x\text{ - 10 = 5x + 15} \\ \text{Subtract 5 x from both sides, we have that:} \\ 6x\text{ - 5x - 10 = 5x - 5x + 15} \\ x\text{ - 10 = 15} \\ \text{Now, add 10 to both sides, we have that:} \\ x\text{ - 10 + 10 = 15 + 10} \\ x\text{ = 25} \\ \text{check:} \\ 6x\text{ - 10 = 5x + 15} \\ \sin ce,\text{ x = 25 , we have that:} \\ 6(25)\text{ - 10 = 5(25) + 15 } \\ 150\text{ - 10 = 125+ 15= 140 ( COR}\R ECT) \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]x\text{ = 25}[/tex]
The measure of three angels of a triangle are 43, 70, and x what is the value of x
Answers
According to the given data we have the following:
measure of three angels of a triangle are 43, 70, x
x?
The sum of the measures of the three angles of the triangle is 180
Therefore, to calculate the value of x we would have to make the following calculation:
43 + 70 + x = 180
113+ x=180
x=180-113
x=67
Therefore, the value of the angle of x would be 67