Answer:
One possible equation is [tex]f(x) = (x + 3)\, (x - 5)[/tex], which is equivalent to [tex]f(x) = x^{2} - 2\, x - 15[/tex].
Step-by-step explanation:
The factor theorem states that if [tex]x = x_{0}[/tex] (where [tex]x_{0}[/tex] is a constant) is a root of a function, [tex](x - x_{0})[/tex] would be a factor of that function.
The question states that [tex](-3,\, 0)[/tex] and [tex](5,\, 0)[/tex] are [tex]x[/tex]-intercepts of this function. In other words, [tex]x = -3[/tex] and [tex]x = 5[/tex] would both set the value of this quadratic function to [tex]0[/tex]. Thus, [tex]x = -3\![/tex] and [tex]x = 5\![/tex] would be two roots of this function.
By the factor theorem, [tex](x - (-3))[/tex] and [tex](x - 5)[/tex] would be two factors of this function.
Because the function in this question is quadratic, [tex](x - (-3))[/tex] and [tex](x - 5)[/tex] would be the only two factors of this function. In other words, for some constant [tex]a[/tex] ([tex]a \ne 0[/tex]):
[tex]f(x) = a\, (x - (-3))\, (x - 5)[/tex].
Simplify to obtain:
[tex]f(x) = a\, (x + 3)\, (x - 5)[/tex].
Expand this expression to obtain:
[tex]f(x) = a\, (x^{2} - 2\, x - 15)[/tex].
(Quadratic functions are polynomials of degree two. If this function has any factor other than [tex](x - (-3))[/tex] and [tex](x - 5)[/tex], expanding the expression would give a polynomial of degree at least three- not quadratic.)
Every non-zero value of [tex]a[/tex] corresponds to a distinct quadratic function with [tex]x[/tex]-intercepts [tex](-3,\, 0)[/tex] and [tex](5,\, 0)[/tex]. For example, with [tex]a = 1[/tex]:
[tex]f(x) = (x + 3)\, (x - 5)[/tex], or equivalently,
[tex]f(x) = x^{2} - 2\, x - 15[/tex].
i will give brand list and hurry pleas
Answer:
3/2 cm/s
Step-by-step explanation:
speed = gradient of the line (slope)
To calculate the slope divide the change in y by the change in x:
(9 - 0) / (6 - 0) = 9/6 = 3/2 cm/s
Find x
1. x + 10 < -7
2. -3x - 4 > 5
Help me please
1)
x+10<-7
bring 10 to the other side
x<-10-7
x<-17
2)
-3x-4>5
bring -4 to the other side
-3x>9
divide -3 at the other side, since it is negative it changes to less than
x<-3
Six days every week, Jill goes to Starbucks to get something. She
alternates in sequence between a Latte, a Mocha, and a Cappuccino,
and always gets the Venti size (20 ounces). The Latte has 240 calories. The Mocha has 340 calories, and the Cappuccino has 150 calories. A
year is approximately 52 weeks long. Consuming an extra 3,500 calories will cause you to gain one pound of fat. How many pounds of fat per year will Jill gain from feeding her Starbucks habit?
How many solutions does this system have?
2 x +3y = -3
3x + 5 = -9
Answer:
x = 12 and y = -9
Explanation:
Given:
2 x +3y = -3
3x + 5y = -9
make x the subject:
[tex]2 x +3y = -3[/tex]
[tex]2x = -3 - 3y[/tex]
[tex]x = \frac{-3 - 3y}{2}[/tex] _____equation 1
[tex]3x + 5y = -9[/tex]
[tex]3x = -9-5y[/tex]
[tex]x = \frac{-9-5y}{3}[/tex] ______equation 2
solve them simultaneously:
[tex]\frac{-9-5y}{3} = \frac{-3 - 3y}{2}[/tex]
[tex]2(-9-5y) = 3(-3-3y)[/tex]
[tex]-18-10y = -9 - 9y[/tex]
[tex]-10y + 9y = -9 + 18[/tex]
[tex]-y = 9[/tex]
[tex]y = -9[/tex]
now solve for x:
[tex]2 x +3y = -3[/tex]
[tex]2x + 3(-9) = -3[/tex]
[tex]2x -27 = -3[/tex]
[tex]2x = -3 + 27[/tex]
[tex]2x = 24[/tex]
[tex]x = 12[/tex]
coordinates where they both intersect is (12,-9) at one point so they have one solution
Answer:
x = 12
y = -9
The system has one solution as it has one point of intersection at (12, -9)
Step-by-step explanation:
Equation 1: [tex]2x + 3y = -3[/tex]
Equation 2: [tex]3x + 5y = -9[/tex]
Rewrite equation 1 to make [tex]x[/tex] the subject:
[tex]2x + 3y = -3[/tex]
[tex]\implies 2x = -3 - 3y[/tex]
[tex]\implies x = -\dfrac32 - \dfrac32 y[/tex]
Substitute this into equation 2 and solve for [tex]y[/tex]:
[tex]3( -\dfrac32 - \dfrac32 y)+5y=-9[/tex]
[tex]\implies -\dfrac92 - \dfrac92 y+5y=-9[/tex]
[tex]\implies -\dfrac92 +\dfrac12 y=-9[/tex]
[tex]\implies \dfrac12 y=-\dfrac92[/tex]
[tex]\implies y=-9[/tex]
Substitute y = -9 into one of the equations to find [tex]x[/tex]:
[tex]2x + 3(-9) = -3[/tex]
[tex]\implies 2x - 27 = -3[/tex]
[tex]\implies 2x = 24[/tex]
[tex]\implies x=12[/tex]
"Point D has the same x-coordinate as the y-coordinate as B same same y-coordinate as the x-coordinate of point A." I need help on C.
Let's name the x-coordinates and y-coordinates
x-coordinate = abscicca y-coordinate = ordinateSo, According to question
Abscicca of Point D = Ordinate of Point BOrdinate of Point D = Abscicca of Point AAbscicca of Point A = 2
Ordinate of Point B = -4
Thus,Point D = (-4,2)
What is the exact volume of the cylinder?
Answer:
pie x r² x h is volume of cylinder
A student calculated the mean of a set of 15 numbers and gets a result of 41.6. In calculating the mean, he inadvertently entered 117 for one of the numbers into his calculator instead of 17. What is the true mean of the data
Answer:
35.93
Step-by-step explanation:
If the mean of 15 numbers is 41.6, the sum of these numbers must be (15)*(41.6) = 624
We n=know one of these numbers is the 117 that was entered by mistake. Subtract that out and replace it with the correct number, 17. In essence we are modifying the number by (-117+17) or -100.
524 is the corrected value. Divide that by 15 to find the ciorrect mean:
(524)/15 = 34.93
Tessa wants to separate 187 ears of corn into bags of 6 ears each. She has 35 bags. Estimate to find whether Tessa has enough bags. Explain.
Answer:
The answer is 228 bags left
HELP Solve for x and PS
Answer:
x = 18 2/3PS = 34 1/3Step-by-step explanation:
You want the values of x and PS for the trapezoid in the figure, given that its perimeter is 228 units.
SymmetryThe trapezoid is shown as an isosceles trapezoid, so PS = RQ. The Triangle RTQ will be repeated on the left side, meaning there is a point T' below point S such that T'P = 4 and T'T = SR = 4x+1.
PerimeterThe perimeter is the sum of side lengths. Working clockwise from the upper left corner this is ...
perimeter = (4x+1) +(2x -3) +4 +(4x +1) +4 +(2x -3) = 12x +4
SolutionSolving for x, we find ...
12x +4 = 228
12x = 224
x = 224/12
x = 18 2/3
And PS is ...
PS = RQ = 2x -3 = 2(18 2/3) -3 = 37 1/3 -3
PS = 34 1/3
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What are the angles for angles 2 through 8?
Please help (NO BOTS)
Answer: angle 2= 145
angle 3= 145
angle 4=35
angle 5=35
angle 6=145
angle 7= 145
angle 8=35
Step-by-step explanation:
look over your angle theorems like the interior angles theorem and the supplementary angle theorem
Quadrilateral RSTU has one pair of opposite parallel sides and one pair of opposite congruent sides as shown.
Quadrilateral R S T U is shown. Sides R U and S T are parallel. The lengths of sides R S and U T are congruent.
Based on the given information, which statement best explains whether the quadrilateral is a parallelogram?
It cannot be determined from the information given.
It is not a parallelogram because the congruent sides cannot be parallel.
It is not a parallelogram because the parallel sides cannot be congruent.
It is a parallelogram based on the single opposite side pair theorem.
Answer:
A It cannot be determined from the information given.
Step-by-step explanation:
Answer:
its A
Step-by-step explanation:
trust
Melissa collected the data in the table. When x = 4, what is the residual? –3 –1 1 3.
The residual value when the value of x = 4 is -1, the correct option is B.
Given
Melissa collected the data in the table.
Residual valueThe difference between the observed value of the dependent variable (y) and the predicted value (ŷ) is called the residual.
The value of x= 4 then the value of residual is given by;
[tex]\rm Residual=Given - predicted \ value[/tex]
Here, given is 9 and the predicted value is 10 for x =4.
Substitute all the values in the formula;
[tex]\rm Residual=Given - predicted \ value\\\\\rm Residual=9-10\\\\\rm Residual=-1[/tex]
Hence, the residual value when the value of x = 4 is -1.
To know more about residual value click the link given below.
brainly.com/question/15996059
Answer:
B
Step-by-step explanation:
(7x2-4x-8) - (x2+6x-1)
Answer:
6x^2-10x-7
Step-by-step explanation:
(7x^2-4x-8) - (x^2+6x-1)
Distribute the minus sign
(7x^2-4x-8) - x^2-6x+1
Combine like terms
(7x^2-x^2 -4x-6x -8+1
6x^2-10x-7
Work out
5/8
×
8/25
Give your answer in its simplest form
[tex]\cfrac{5}{8}\cdot \cfrac{8}{25}\implies \cfrac{5}{25}\cdot \cfrac{8}{8}\implies \cfrac{1}{5}\cdot 1\implies \cfrac{1}{5}[/tex]
Adjust the equations to create three different parabolas that pass through the points.
Answer:
Make all of the +/-2 values into -3,+4
Step-by-step explanation:
This is because the x intercept values for a parabola are where the equation equals zero, by making the equations -3 and +4, the equations will give zero values at -4 and plus 3 when they are set equal to zero, I can specify further if need be.
I need help please someone
Answer:
A- not sure how to show u
B- 50% or 1/2
C-33% or 1/3
D- 40% or 2/5 im not sure
Step-by-step explanation:
what is the reciprocal of -0.06
Answer:
-16.666
Step-by-step explanation:
You can find the reciprocal by turning the intended fraction upside down.
[tex]\frac{-0.06}{1}[/tex] ⤭ [tex]\frac{1}{-0.06}[/tex] = [tex]\frac{100}{-6}[/tex] = [tex]\frac{50}{-3}[/tex] = -16.6666666667
Please help with mark brainliest if correct!!! ASAP
Answer:
2 mm: 1 m
Step-by-step explanation:
The scale drawing has the length of the soccer field as 232 millimetres.The actual field is 116 meters long.That is, the same soccer field has different lengths in actual and in a map.
These scale and actual lengths must be related, and they are related to each other by what we call the scale ratio.
Scale ratio = dimensions in a drawing : actual dimensions
= 232mm : 116m
(we divide this by 116 to get 2)
= 2mm : 1m
Use the diagram to complete the statement.
measure of angle ECD
Answer:
∠ECD = 82°
Step-by-step explanation:
Alternate Interior Angles Theorem : when two parallel lines are cut by a transversal, the alternate interior angles are congruent. Alternate angles form a Z shape and are sometimes called "Z angles".
Therefore,
∠CDF = ∠GBC = 45°
∠CEF = ∠GAC = 53°
The sum of the interior angles of a triangle is 180°
⇒ ∠ECD + ∠CDF + ∠CEF = 180
⇒ ∠ECD + 45 + 53 = 180
⇒ ∠ECD = 180 - 45 - 53 = 82°
In ∆ABC
m<C be x[tex]\\ \tt\longrightarrow x+53+45=180[/tex]
[tex]\\ \tt\longrightarrow x+98=180[/tex]
[tex]\\ \tt\longrightarrow x=180-98[/tex]
[tex]\\ \tt\longrightarrow x=82[/tex]
Now
m<ECD and m<ACB are opposite hence equal
find rate of change!! basic algebra
The slope of these lines is -17/7
OABC is a trapezium.
D is the point on OB such that OD : DB = 2:3
E is the point on BC such that BE : EC = 1:4
Work out the vector of DE in terms of a & b. Give your answer in its simplest form.
Answer:
DE = 2/5a + bStep-by-step explanation:
Find OB:
OB = a + bFind BC:
OB + BC = OCa + b + BC = 3bBC = 2b - aFind DB:
OD/DB = 2/3 ⇒ OD + DB = OB ⇒ 2x + 3x = OB ⇒ 5x = OB ⇒ x = OB/5DB = 3x = 3/5 OB = 3/5(a + b)Find BE:
BE/EC = 1/4 ⇒ BE + EC = BC ⇒ x + 4x = BC ⇒ 5x = BC ⇒ x = 1/5 BCBE = x ⇒ BE = 1/5 BC ⇒ BE = 1/5(2b - a)Find DE:
DE = DB + BEDE = 3/5(a + b) + 1/5(2b - a) DE = 1/5(3a + 3b + 2b - a)DE = 1/5(2a + 5b)DE = 2/5a + bIf one book is 55 dirham then what is the cost of 20 books
Answer:
1100 dirham
Step-by-step explanation:
If one book is 55 dirham, then you multiply that by 20 to get the total cost.
(If you are supposed to go from dirham to something else, then I'm sorry I don't know)
Hope this helps!
A__ is two or more atoms joined together
Answer: c
Step-by-step explanation:
The answer Is C molecule
Vhat is the length of the unknown leg in the right triangle?
25 m
b
20 m
o 5 m
5 m
o 45 m
15 m
Mark this and return
Save and Exit
Next
Answer:
15m
Step-by-step explanation:
to answer this question, we need to use pythagorean theorem. this theory says:
a² + b² = c²
so, let’s work out b.
a² + b² = c²
20² + b² = 25²
20 x 20 = 400. 25 x 25 = 625.
400 + b² = 625.
we want to solve for b, which means to get b in it’s own, so we are going to get rid of the 400 on both sides, leaving just b² on the one side.
625-400=225.
b² = 225
b = √225
b = 15 :)
hope this helps!!!!
The bottom of a rectangular swimming pool has an area of 512 feet2. If the length of the
pool is 16 feet, what is the width?
I need help with this question please.
Answer:
1/5x dogs were on a leash
Step-by-step explanation:
To work through this problem we have to keep in mind that x represents the number of dogs at the park.
1/5 of x dogs are leashed.
Therefore, we can conclude that the answer is 1/5x.
I have no idea if the picture of the dogs was meant to give a clue but hope this helps :)
There are 8 girls and 5 boys on the math team. Which ratio correctly describes the relationship between boys and girls
on the math team?
Answer:
8:5
Step-by-step explanation:
Calculate how much more or less the muse will earn per month compared to selina, is selina salary is R234740
Answer:
um yes to the opreations sjut ad
solve for x. show your solution
i’ll mark as brainiest
Answer:
x=12
Step-by-step explanation:
Using the external angle theorem (external angle = sum of interior angles that are NOT adjacent to the external angle you are finding), we can set up an equation...
140=3x+4+8x+4
Start by combining like terms...
140=11x+8
Subtract 8 from both sides
132=11x
Divide both sides by 11
x=12
The function f(x) = 1/x-3 is defined for all real numbers except when x equals
1) 0
2) 3
3) --
4) 3
lol
Answer:
except when x = 3
Step-by-step explanation:
f(x) = [tex]\frac{1}{x-3}[/tex]
the denominator cannot be zero as this would make f(x) undefined.
Equating the denominator to zero and solving gives the value that x cannot be.
x - 3 = 0 ⇒ x = 3 ← excluded value
f(x) is defined for all real numbers except when x = 3