Explication étape par étape:
Étant donné la fonction polynomiale f (x) = -2x² + 4x + 6. Pour vérifier si f (-1) est un facteur de l'expression, nous devons montrer que f (-1) est équivalent à zéro. S'il est nul, donc x + 1 est un facteur du polynôme.
Preuve
f (x) = -2x² + 4x + 6
f (-1) = -2 (-1) ² + 4 (-1) +6
f (-1) = -2 (1) -4 + 6
f (-1) = -2-4 + 6
f (-1) = -6 + 6
f (-1) = 0
Puisque f (-1) = 0, donc x + 1 est un facteur du polynôme.
Ensuite, il faut obtenir l'autre racine du polynôme. Pour obtenir cela, nous devons factoriser la fonction polynomiale donnée.
Soit f (x) = 0
-2x² + 4x + 6 = 0
multiplier par -1
2x²-4x-6 = 0
diviser par 2
x²-2x-3 = 0
x²-3x + x-3 = 0
x (x-3) +1 (x-3) = 0
(x + 1) (x-3) = 0
x + 1 = 0 et x-3 = 0
x = 1 et x = 3
Par conséquent, l'autre racine du polynôme en dehors de 1 est x = 3
The function A = 28x- x^2, where x = width, gives you the area of a dog pen in square feet. What is the maximum area? Round to the nearest tenth as necessary
Answer:
max A=42x
Step-by-step explanation:
given the following formula, solve for t
Answer:
C
Step-by-step explanation:
Given
v = u + at ( subtract u from both sides )
v - u = at ( isolate t by dividing both sides by a )
[tex]\frac{v-u}{a}[/tex] = t
A teacher chooses two students in a class of 15 girls and 10 boys. The students are randomly chosen. What is the probability that the teacher chooses two girls?
The probability that the teacher chooses two girls is 3 / 5.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favorable outcomes / Number of sample
Given that a teacher chooses two students in a class of 15 girls and 10 boys. The probability is calculated as:-
P = 15 / 25
P = 3 / 5
Hence, the probability is 3 / 5.
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please help i need it quickly i only have 5 minutes left. ill give brainliest.
Answer:
A
B
C
Step-by-step explanation:
A
11=4(7)-17
11=28-17
11=11
B
-13=4(1)-17
-13=4-17
-13=-13
C
-1=4(4)-17
-1=16-17
-1=-1
Harper is a sales person who sells computers at an electronics store. She makes a base pay amount of $100 per day regardless of sells and she earns a commission of 1% of the dollar amount of all sells that she makes. Write an equation for P, in terms of x, representing harpers total pay on a day on which she sells x dollars worth of computers.
Answer:
P=0.01x+100
Step-by-step explanation:
HELP ASAP
How much interest is earned on a $500 investment made at a 3.5% simple interest
rate over the course of 2 years?
A$3500
B $350
C$35
D$3.50
Answer:
C
Step-by-step explanation:
500* (0.035)
17.5*2
35
an obese man, 5'0 tall and 160 pounds, sets a long-term goal to lose 40 pounds. What is a reasonable benchmark he might set for himself
Answer: Lose 10 pounds in 3 months
Step-by-step explanation: 5'0, 160, 40 ~ 10 > 3 Months
Solve the following quadratic equation:
the following quadratic equation: 2x2 - 52 + 2 = 0
Answer:
x₁ = -5, x₂ = 5Step-by-step explanation:
[tex]2x^2 - 52 + 2 = 0\\\\2x^2-50=0\\\\x^2-25=0\\\\x^2=25\\\\x=5\qquad\vee\quad\ x=-5[/tex]
A building has the shape of a pyramid with a square base. The midsegment parallel to the ground of each triangular face of
the pyramid has a length of 58 feet. The perimeter of the base of the pyramid is
feet.
Answer:
The length of the base the pyramid is 116 feet.
Step-by-step explanation:
See the diagram attached to this answer.
Let Δ OAB is the side triangle of the square pyramid, and A'B' is the mid segment parallel to the ground with length of 58 feet.
Now, Δ OAB and Δ OA'B' are similar triangle and the length of sides of the triangle Δ OA'B' are in the same ratio with the corresponding sides of Δ OAB.
Hence,
⇒ AB = 2 × 58 = 116 feet.
The length of the base the pyramid is 116 feet. (Answer)
Given the function f(x) = 4x evaluate
f(-2)
Answer:
the answer =-8
Step-by-step explanation:
you subsitute -2 for x so its 4(-2) which is -8
Answer:
Given value x=-2, just substitute it to [tex]4^{x}[/tex]
= [tex]4^{-2}[/tex] (this uses the property [tex]a^{-m}=\frac{1}{a^{m} }[/tex])
= This results in:
[tex]\frac{1}{4^{2} } = \frac{1}{16 }[/tex]
It might be hard to see but please help me out!
Answer:
X: (-2) (-1) (0) (1) (2)
y: (5) (4) (5) (8) (13)
Step-by-step explanation:
╰(▔∀▔)╯ (─‿‿─) (*^‿^*) ヽ(o^ ^o)ﾉ (✯◡✯) (◕‿◕) (*≧ω≦*)
Which of the following numbers can be expressed as repeating decimals? (5 points) 3 over 7 , 2 over 5 , 3 over 4 , 2 over 9
Answer:
3/7 and 2/9 are repeating decimals.
Step-by-step explanation:
which expressions are equal to 3/5 × 6
a. 3 × ( 6 ÷ 5 )
b. 3 ÷ (5 × 6 )
c. ( 3 × 6 ) ÷ 5
d. 3 × 6/5
Answer:
A & C & D
Step-by-step explanation:
A & C & D both show the commutative property of multiplication and therefore is the correct answer because 3/5(6) = 18/5 and 3(6/5) is also 18/5.
3 x (6÷5) is also 18/5
(3×6)÷5 is also 18/5
Theequationforlineucanbewrittenasy = 6x + 6 . Line v , whichisperpendiculartoline u , includes the point (10, –5) . What is the equation of line v ? Write the equation in slope-intercept form. Write the numbers in the equation as proper fractions, improper fractions, or integers.
Answer:
[tex]y=\frac{-1}{6}x-\frac{10}{3}[/tex]
Step-by-step explanation:
Slope intercept form of the equation of a line is [tex]y=mx+b[/tex] where m denotes the slope of line and [tex]b[/tex] denotes the y-intercept.
Equation of a line u is [tex]y=6x+6[/tex]
Here, slope of line u = m = 6
As the line v is perpendicular to line u, product of slopes of both the lines is equal to [tex]-1[/tex].
Slope of line v [tex]=\frac{-1}{6}[/tex]
So, slope intercept form of the line v is [tex]y=\frac{-1}{6}x+b[/tex]
As point [tex](10,-5)[/tex] lies on the line v, put [tex](x,y)=(10,-5)[/tex] in equation [tex]y=\frac{-1}{6}x+b[/tex]
[tex]-5=\frac{-1}{6}(10)+b\\-5=\frac{-5}{3}+b\\ -5+\frac{5}{3}=b\\\frac{-15+5}{3}=b\\\\\frac{-10}{3}=b[/tex]
Equation of line v is [tex]y=\frac{-1}{6}x-\frac{10}{3}[/tex]
24 is equal to 25% of a number n. Write and solve an equation to find n. Write the percent as a Decimal. PLEASE HELP ME
Answer:
Equation: 25% x n = 24
n = 96
Step-by-step explanation:
Because of means to multiply 25% OF n would mean you multiply to solve for n you would do the opposite which is dividing. 25% is the same as .25 so you would do...
24 ÷ .25 = 96
So 96 = n
Hope that helps and have a great day!
A circle is centered at the point O (0,0) and has a radius of the square root of 38?
Where’s does the K (6,1) lie?
Answer:
The point (6,1) lies inside the circle.
Step-by-step explanation:
Equation of a Circle
A circle centered at the point (h,k) and with radius r, can be expressed with the equation:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
The center of the given circle is (0,0) and the radius is [tex]r=\sqrt{38}[/tex], thus the equation of the circle is:
[tex](x-0)^2+(y-0)^2=(\sqrt{38})^2[/tex]
Simplifying:
[tex]x^2+y^2=38[/tex]
Each point (x,y) meeting the condition of the equation lies exactly on its circumference. For example, the point [tex](\sqrt{2},6)[/tex] belongs to the circumference, but the origin (0,0) is inside the circle, and the point (5,5) is outside the circle.
We can tell the difference by evaluating the equation at each point. For the first point [tex](\sqrt{2},6)[/tex], the equation is:
[tex](\sqrt{2})^2+6^2=2+36=38[/tex]
The equation is satisfied.
For the origin (0,0):
[tex]0^2+0^2=0[/tex]
For the point (5,5):
[tex]5^2+5^2=50[/tex]
We can conclude that if the left side is greater than 38, the point is outside the circle, if it's less than 38, the point is inside the circle.
Let's test the point (6,1):
[tex]6^2+1^2=37[/tex]
The point (6,1) lies inside the circle.
please help me? im DESPERATE!!!!
Convert 8 centimeters to millimeters.
Answer:
80mm
Step-by-step explanation:
As 1 cm = 10 mm
8 cm=80 mm
Answer:
80 millimeters
Step-by-step explanation:
Well you convert it
plz help ASAP matswatch
Answer:
Step-by-step explanation:
derive the equation of a parabola with a focus of (-7,5) and a directrix of y=-11
I need help with this question
Answer:
The equation of the parabola is;
(y + 11)^2/120 = (x + 7)^2 + (y-5)^2
Step-by-step explanation:
Here, we are given the focus (-7,5) and the directix y = -11
We proceed to find the equation of the parabola
That would be in the form;
(y- mx - b)^2 /m^2 + 1 = (x- h)^2 + (y-k)^2
Let’s write the directix in the form y = mx + b
This shows that m = 0 and b = -11
Also h = -7 and k = 5
So let’s substitute;
(y + 11)^2 /(-11^2 + 1) = (x+7)^2 + (y-5)^2
= (y + 11)^2/120 = (x + 7)^2 + (y-5)^2
Answer:
★ The answer is down BELOW
EQUATION : (y + 11)^2/120 = (x + 7)^2 + (y-5)^2
Step-by-step explanation:
Hope you have a great day
PLEASE HELP IF YOU CANNNN
Answer:
Im pretty sure it would land in quadrant 2
Step-by-step explanation:
Write an expression from the description. Then
evaluate the expression.
9 more than the quotient of -36 and -4.
(-36 ÷ -4) + 9
The expression equals 18.
Which quadratic expression represents the product of these factors?
(2x + 5)(7 − 4x)
A.
-8x2 + 34x − 35
B.
-8x2 + 6x − 35
C.
-8x2 − 6x + 35
D.
-8x2 − 34x + 35
The answer is c -8x^2-6x+35
May someone help me with this question?
Evaluate the following expression.
1/2 + 2/3 divided by 1/6
What is 1 2/3 - 2 1/3?
Answer:
-0.6666
Step-by-step explanation:
Answer:
-2/3
Step-by-step explanation:
Make the fractions into improper fractions. Then you procede to subtract from left to right from the top. The 1 2/3 becomes 5/3 and the 2 1/3 becomes 7/3 and when you subtract your answer is -2/3
1) Ao somar o quíntuplo de um número com 5², o total é 300. Considerando x como a incógnita. Qual o valor de x?
a)25
b)5
c)325
d)55
2) O triplo de um número aumentado do dobro desse mesmo número é igual a 100. Considerando a incógnita como y, qual o valor de y?
a)100
b)20
c)24
d)5
3) A metade de um número, menos 21, é igual a -5. Considere x o valor a ser determinado. É correto afirmar que x é igual a?
a)52
b)-32
c)32
d)16
4)Ao resolver a expressão y - 30 = 3 . 15, qual o valor de y?
a)75
b)65
c)55
d)45
5)Observe a equação 3x + 72 = 104. Qual descrição abaixo corresponde a ela?
a)A soma entre o triplo de um número e 72 é igual a 104
b)O triplo de um número subtraído de 104 é igual a 72
c)O triplo de 3 é igual a 104 somado a 72
6) Quando subtraímos 50 do triplo um número, obtemos 40. Qual equação representa essa afirmação?
a)3x = 50 - 40
b)3x - 50 = 40
c)3x = 40 - 50
7) Determine a solução das seguintes equações do 1º grau com uma incógnita. 63y + 75 = 327. Qual o valor de y=?
a)2
b)4
c)6
d)8
8) Determine a solução das seguintes equações do 1º grau com uma incógnita. 13x - 100 = 8x. Quanto vale x=?
a)18
b)19
c)20
d)21
9) Determine a solução das seguintes equações do 1º grau com uma incógnita. 10 (x + 1) - 8 (x - 2)= 30 . Quanto vale x=?
a)1
b)2
c)4
d)8
10) Determine a solução das seguintes equações do 1º grau com uma incógnita. 10 + 9y = 100. Quanto vale y=?
a)9
b)10
c)11
d)12
Answer:
Huh?
Step-by-step explanation:
Select all that apply.
Which of the following name an angle in the drawing?
Answer:
ECB and CDE
Step-by-step explanation:
the others arent the same
If a track is 400 meters around, how many laps around the track would it take to run 3.1 miles round to the nearest tenth
Answer:
Step-by-step explanation:
12.5
Number of laps in given distance is 12.5 laps.
Given:
Length of a track = 400 meter
Total distance = 3.1 miles
Find:
Number of laps in given distance
Computation:
We know that
1 miles = 1609.34 meter
So,
Total distance = 3.1 miles
Total distance = 3.1 × 1609.34
Total distance = 4988.954
Number of laps in given distance = 4988.954 / 400
Number of laps in given distance = 12.4723
Number of laps in given distance = 12.5 laps (Approx.)
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Which of the following is a line perpendicular
to y = 3x-7?
Answer:
y=-1/3x-7
Step-by-step explanation:
Change the sign of x and flip the slope. 3/1 equals -1/3.
