Answer:
[tex]3x^2-10x+8=(x-x_1)(x-x_2)=(x-2)(x-\frac{4}{3})[/tex]
Step-by-step explanation:
The general form of a quadratic polynomial is given by:
[tex]ax^2+bx+c[/tex] (1)
You have the following polynomial:
[tex]3x^2-10x+8[/tex] (2)
In order to complete the factorization you can use the quadratic formula, to obtain the roost of the polynomial. The quadratic formula is given by:
[tex]x_{1,2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex] (3)
By comparing the equation (1) with the equation (2) you obtain:
a = 3
b = -10
c = 8
Then, you replace these values in the equation (3):
[tex]x_{1,2}=\frac{-(-10)\pm \sqrt{(-10)^2-4(3)(8)}}{2(3)}\\\\x_{1,2}=\frac{10\pm2}{6}\\\\x_1=2\\\\x_2=\frac{4}{3}[/tex]
Then, the factorization of the polynomial is:
[tex]3x^2-10x+8=(x-x_1)(x-x_2)=(x-2)(x-\frac{4}{3})[/tex]
The value of r represents the distance from a point to the pole when plotting that point in polar coordinates. True or False?
Answer:
True, r represents the distance from a point to the pole when plotting that point in polar coordinates.
Step-by-step explanation:
Given: The statement '' The value of r represents the distance from a point to the pole when plotting that point in polar coordinates ''
To state: whether the given statement is true or false
Solution:
In the cartesian coordinate system, any point is represented by the coordinates [tex](x,y)[/tex]
In polar-coordinates system, distance of the point from the origin (pole)(r) and the angle [tex](\theta)[/tex] that the line joining the point to the origin makes with the positive x -axis are used as polar coordinates. Polar coordinates are of form [tex](r,\theta)[/tex]
True, r represents the distance from a point to the pole when plotting that point in polar coordinates.
Answer:
true
Step-by-step explanation:
trust
After the bank cashed a check Maureen wrote for $60, her balance was Negative 14 dollars. The equation b + (negative 60) = negative 14 can be used to represent this situation, where b is Maureen’s balance, in dollars, before the check was cashed. Maureen attempted to solve the equation using the steps below. b + (negative 60) = negative 14. Subtract 60 from both sides. B = negative 74. What error, if any, did Maureen make? Maureen’s work is correct, and her original balance was -$74. Maureen should have added 60 to both sides. Maureen should have added 14 to both sides. Maureen made a computational error when she subtracted 14 minus 60.
Answer:
-74
Step-by-step explanation:
Answer: -74
Step-by-step explanation:
find an equation of cosine function with maximum of 7, minimum of -7 and period of 7
Answer: [tex]\bold{y=7cos\bigg(\dfrac{2\pi}{7}x\bigg)}[/tex]
Step-by-step explanation:
y = A cos (Bx - C) + D
A = amplitude (vertical stretch)Period = 2π/BC/B = phase shiftD = vertical shiftThe minimum is -7 and the max is 7 so A = 7 and D = 0
Period is 7. Since P = 2π/B then 7 = 2π/B --> B = 2π/7
Nothing was stated about a phase shift so you can use any value for C. I chose C = 0.
Now, input A = 7, B = 2π/7, C = 0, & D = 0 into the equation
[tex]y=7\cos\bigg(\dfrac{2\pi}{7}x-0\bigg)+0\\\\\\\text{Simplify}:\\y=7\cos\bigg(\dfrac{2\pi}{7}x\bigg)[/tex]
In a 40% off sale, a dress was £45. Work out the original price
Answer:
40%=45
So, 100%=45*100/40
=112.2
PLEASE SEE PIC BELOW
Please answer correctly !!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!
Answer:
c
Step-by-step explanation:
they share the same min of -3
Answer:
The minimum values are equal
Step-by-step explanation:
The minimum for f(x) = (4,-3) since the parabola is written in vertex form
y = a(x-h)^2 +k
The minimum is at x=4 the the y value is -3
Looking at the graph for g(x) the minimum is at x=-3 y = -3
Since the y values are equal
The minimum values are equal
Work out the area of the given shape ;)
1. 36 sq m
2. 24 sq m
3. 48 sq m
Answer:
The answer would be, 36 sq m
What is BE in the figure?
Answer:
i think its A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
write a quadratic function f whose zeros are -2 and -9
Answer:
f(x) = x^2 + 11x + 18.
Step-by-step explanation:
As the zeroes are -2 and -9 the factored form is
f(x) = a(x - (-2))(x - (-9)) where a is some constant.
As we want any quadratic function with theses zeros we can let a = 1 so:
f(x) = (x + 2)(x + 9)
f(x) = x^2 + 2x + 9x + 18
f(x) = x^2 + 11x + 18.
The required quadratic function is given as x²+11x+18 = 0,
Given that,
To write a quadratic function f whose zeros are -2 and -9
Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
x = -2 and x = -9
x 2 = 0 and x + 9 = 0
The function is given as,
(x + 2)(x + 9) = 0
x²+11x+18 = 0,
Thus, the required quadratic function is given as x²+11x+18 = 0,
learn more about function here:
brainly.com/question/21145944
#SPJ2
HELP! Thank you in advance <3
Answer:
WALK=9 PUPILS
BUS=12 PUPILS
CAR=4 PUPILS
BIKE=4 PUPILS
Step-by-step explanation:
TOTAL=360/10 = 36 120+90=210
BUS=120/10=12 360-210=75/2=37.5
WALK=90/10=9
CAR=37.5/10=3.75=4
BIKE=37.5/10=3.75=4
What is the range of the function?
(1,2) (2,4) (3,9) (4,16)
Answer:
{ 2 , 4 , 9 , 16 }
Step-by-step explanation:
Answer:
range ={ 2,4,9,16}
Step-by-step explanation:
range is related to y coordinate of the points
Show all work to identify the asymptotes and zero of the function f of x equals 5 x over quantity x squared minus 25
Answer: VA: x = {-5, 5), HA: y = 0, Zeros: x = 0
Step-by-step explanation:
[tex]f(x) = \dfrac{5x}{x^2-25}[/tex]
Vertical asymptotes: The denominator cannot equal zero.
x² - 25 = 0
(x - 5)(x + 5) = 0
x = 5, x = -5
Horizontal Asymptote: Let m represent degree of numerator and n represent the degree of the denominator.
If m > n then NO asymptoteIf m = n, then y = coefficient of m ÷ coefficient of nIf m < n, then y = 0For the given equation, m = 1 and n = 2 so we use option 3 --> y = 0
Zeros: Set the equation equal to zero and solve for x.
[tex]0=\dfrac{5x}{x^2-25}[/tex]
Multiply both sides by x²- 25 --> 0 = 5x
Divide both sides by 5 --> 0 = x
Using function concepts, it is found that:
The zero of the function is [tex]x = 0[/tex].The vertical asymptotes are [tex]x = \pm 5[/tex].The horizontal asymptote is [tex]y = 0[/tex].The function is given by:
[tex]f(x) = \frac{5x}{x^2 - 25}[/tex]
Applying the subtraction of perfect squares, the function will be given by:
[tex]f(x) = \frac{5x}{(x - 5)(x + 5)}[/tex]
The zero is the value of x for which:
[tex]f(x) = 0[/tex]
In a fraction, it is when the numerator is zero, thus:
[tex]5x = 0[/tex]
[tex]x = \frac{0}{5}[/tex]
[tex]x = 0[/tex]
The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator, thus:
[tex](x - 5)(x + 5) = 0[/tex]
[tex]x = \pm 5[/tex]
The horizontal asymptote is:
[tex]y = \lim_{x \rightarrow \infty} f(x)[/tex]
Hence:
[tex]y = \lim_{x \rightarrow \infty} \frac{5x}{x^2 - 25} = y = \lim_{x \rightarrow \infty} \frac{5x}{x^2} = y = \lim_{x \rightarrow \infty} \frac{5}{x} = 0[/tex]
A similar problem is given at https://brainly.com/question/23690889
Please answer CORRECTLY !!!!!! Will mark BRIANLIEST !!!!!!
Answer:
you should drag to x axis #3
which graph represents as a function of length of the trip
Which first step for solving the given system using substitution results in an equation without fractions?
-9x4y - 10
-9x+3y3
Answer:
The step to take to avoid fraction is to solve for y in equation 2
Step-by-step explanation:
Given
-9x+ 4y =- 10
-9x+ 3y = 3
Required:
Step for solving using substitution (avoiding fraction)
Let -9x+ 4y =- 10 represent equation 1
and -9x+ 3y = 3 represent equation 2
The following points are to be noted
Solving for x or y in equation 1 will definitely lead to having fractionsSolving for x in equation 2 will also lead to having fractionsHaving said that, the step to take to avoid fraction is to solve for y in equation 2
Check
[tex]-9x+ 3y = 3[/tex]
Add 9x to both sides
[tex]9x-9x+ 3y = 3 + 9x[/tex]
[tex]3y = 3 + 9x[/tex]
Divide through by 3
[tex]\frac{3y}{3} = \frac{3 + 9x}{3}[/tex]
[tex]y = \frac{3 + 9x}{3}[/tex]
Split fraction
[tex]y = \frac{3}{3} + \frac{9x}{3}[/tex]
[tex]y = 1 + 3x[/tex]
At the point, the expression of y can then be substituted in equation 1
Answer: solve for y in the second equation
Step-by-step explanation:
I got it right on edenuity
Helppppppppp pleaseeeeeeeeeee
Answer:
ok
Step-by-step explanation:
Need help will give brainliest
Answer:
1) Step 1- Question. The "thing" that you want to know. ...
Step 2-Research. Conduct research. ...
Step 3-Hypothesis. Educated guess or prediction of the outcome experiment.
Step 4-Experiment. Test the hypothesis.
Step 5-Observations.
Step 6-Results/Conclusion. Determine if your hypothesis was correct or not.
Step 7- Communicate.
2) Being able to communicate the relevance and impact of their ideas and discoveries can enhance scientists' ability to secure funding or find a job. It allows them to write better and more comprehensible research papers.
3) 1) People should be treated as autonomous.
2) People with diminished autonomy should be protected.
3) Do no harm.
4) Maximize benefits for participants and minimize risks for participants.
Step-by-step explanation:
Which equations represent the line that is parallel to 3x − 4y = 7 and passes through the point (−4, −2)? Select two options. y = –Three-fourthsx + 1 3x − 4y = −4 4x − 3y = −3 y – 2 = –Three-fourths(x – 4) y + 2 = Three-fourths(x + 4
Answer:
3x-3y=-4 and y+2=3/4x+4
Step-by-step explanation:
parallel line equations have the same slope. just find the equation that also has positive 3 in this problem
Answer:
B & D
Step-by-step explanation:
What is the value of the expression, written in standard form? ASAP!
Answer:
200
Step-by-step explanation:
[tex]\dfrac{(6.6\times 10^{-2})}{(3.3\times 10^{-4})}= \\\\\\\dfrac{6.6}{3.3}\times \dfrac{10^{-2}}{10^{-4}}=\\\\\\2\times 10^{-2-(-4)}= \\\\2\times 10^2=\\\\200[/tex]
Hope this helps!
is 10.97846727460 rational or irrational
Answer:
Step-by-step explanation:
Answer:
Rational
Step-by-step explanation:
Because the decimal places stop, it is rational. Remember, an Irrational number is non-repeating and non-terminating. Since the number terminates, it is rational
20 is 40 percent of??? please need answer
Answer:
x = 50
Step-by-step explanation:
Let x be the original number.
This question can be expressed as:
0.4x = 20
0.4 of the original number is 20.
Now, we can directly solve for x:
4x = 200
x = 50
Answer:
8
Step-by-step explanation:
40 times 0.20 is 8.
You can also use 40 percent of 20, which is also 8, but the original is easier to comprehend.
Point S lies between points R and T on .
If RT is 10 centimeters long, what is ST?
2 centimeters
4 centimeters
6 centimeters
8 centimeters
Answer:
the value of line ST is 6 centimeters long
Step-by-step explanation:
The attached image in conjunction with the question is shown in the file below.
We can see from the RT segment that the equation given can be expressed as:
[tex]\mathbf{2x+3x = 10}[/tex]
so; if we solve for x ; we have ;
[tex]\mathbf{5x= 10}[/tex]
divide both sides by 5 ; we have:
[tex]\mathbf{\dfrac{5x}{5}= \dfrac{10}{5}}[/tex]
[tex]\mathbf{x=2}[/tex]
However ; the value of ST is represent by the information:
[tex]\mathbf{ ST = 3x}[/tex]
replcaing the value for x; we have :
[tex]\mathbf{ ST = 3*2}[/tex]
[tex]\mathbf{ ST = 6}[/tex]
Thus, the value of line ST is 6 centimeters long
Answer:
C. 6 centimeters
May I have brainliest please? :)
see picture for question
Answer:
6.
Step-by-step explanation:
Both of the arcs that subtend the segments are congruent. By definition, both segments are congruent as well.
Since the length of segment EG is 6, the length of segment FG must be 6.
I hope this helps!
THE is the right question not the last one
Answer:
6
Step-by-step explanation:
1 1/2 = 3/2
3/2 / 1/4 = 3/2 * 4 = 12 / 2 = 6
Answer:
6
Step-by-step explanation:
One recipe uses 1/4 cup of red onions.
They have 1 1/2 cups of red onions.
We need to divide 1 1/2 by 1/4.
First, we convert the mixed numeral into a fraction. Then, to divide by a fraction, we multiply by the reciprocal of the fraction.
[tex] 1 \dfrac{1}{2} \div \dfrac{1}{4} = [/tex]
[tex] = \dfrac{1 \times 2 + 1}{2} \div \dfrac{1}{4} [/tex]
[tex] = \dfrac{3}{2} \times \dfrac{4}{1} [/tex]
[tex] = \dfrac{12}{2} [/tex]
[tex] = 6 [/tex]
The original price of a pair of jeans is $32. The sale price is 15%off the original price. What is the amount off the original price?
Answer:
4.8
Step-by-step explanation:
Multiply the Price Percentage by the Original Price
Multiply the original price and the percentage that represents the sale price; the result is the sale price of the blazer in dollars: $90 × 0.7 = $63. So if the blazer is on sale for 30 percent off, you'll pay the remaining 70 percent of the price, which is $63.
The length plus the width of a rectangle is 10. Let x represent the length. The equation for the area y of the
rectangle is y= x(10- x). The y value of the vertex gives the
value of the
of the rectangle.
Answer:
length of rectangle = 5
width of rectangle = 5
Area of rectangle = 25
Step-by-step explanation:
Since the length of the rectangle is "x", and the value of the area is given by the product of the length "x" times the width "10-x", indeed, the area "y" of the rectangle is given by the equation:
[tex]y=x\,(10-x)=10x-x^2[/tex]
Now, they tell us that the area of the rectangle is such that coincides with the maximum (vertex) of the parabola this quadratic expression represents. So in order to find the dimensions of the rectangle and therefore its area, we find the x-coordinate for the vertex, and from it, the y-coordinate of the vertex, which is the rectangle's actual area.
Recall that the formula for the x of the vertex of a quadratic of the form :
[tex]y=ax^2+bx+c[/tex]
is given by the formula:
[tex]x_{vertex}=-\frac{b}{2\,a}[/tex]
which in our case gives:
[tex]x_{vertex}=-\frac{b}{2\,a}\\x_{vertex}=-\frac{10}{2\,(-1)}\\x_{vertex}=5[/tex]
Therefore, the length of the rectangle is 5, and its width (10-x) is also 5.
The area of the rectangle is therefore the product of these two values: 5 * 5 = 25
Which should coincide with the value we obtain when we replace x by 5 in the area formula:
[tex]y=10x-x^2\\y=50-(5)^2\\y=50-25\\y=25[/tex]
Please help! Correct answer only please! I need to finish this assignment by today.
On a residential single lane road there was a wreck that backed up traffic for 4 miles. 70% of the traffic consists of cars and 30% of the traffic consists of trucks. the average distance between vehicles is 3 feet. the average length of a car is 13.5 feet and the average length of a truck is 20 feet. estimate how many vehicles are stuck in the traffic jam.
(hint: there are 5280 feet in 1 mile)
A) 276
B) 896
C) 1172
D) 1412
Please answer correctly !!!!!!!! Will mark brainliest !!!!!!!!!!!!!!
Add 1 to both sides
Multiply both sides by 4
Take the square root of both sides
Subtract 5 from both sides
In this problem, you are trying to isolate the x. In order to do that you have to get rid of all the other numbers surrounding it. The first thing you're going to do is move the 1. To get rid of the -1 you have to do a +1. What you do to one side you have to do to the other. Therefore, you have to add +1. Next, you will move the 1/4 by multiplying by the reciprocal which is 4 (because 1/4 x 4 = 1, this gets rid of the 1/4 on the left side). After that you will do the opposite of square, which is to take the square root. Lastly, you will subtract the five for the same reason you added the 1.
HELP! 30 pts!
1. Write the point-slope form of the equation of a line with slope 2/5 that passes through the point (-3,-6)
2. Write the slope-intercept form of the equation for a line with slope 1/3 and y-intercept at (0,-2/5)
Answer: y-2=2/5(x-17), y=1/3x-2/5
Step-by-step explanation:
Answer:
1.)y+6=2/5(x+3)
2.)y=1/3x-2/5
Step-by-step explanation:
Helps please.........
Answer:
The answer would be C
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
[tex]\sqrt{\dfrac{36}{25}}=\sqrt{\dfrac{6^2}{5^2}}=\dfrac{6}{5}[/tex]
Therefore, the correct answer is choice C. Hope this helps!