Given:
A quadratic function has x-intercepts 2 and 6 and its vertex is (4, 8).
To find:
The corresponding quadratic expression.
Solution:
If graph of a function intersect the x-axis at c, then (x-c) is a factor of the function.
A quadratic function has x-intercepts 2 and 6. It means (x-2) and (x-6) are two factors of the required quadratic function.
The function is defined as:
[tex]P(x)=a(x-2)(x-6)[/tex] ...(i)
Where, a is a constant.
The vertex of the quadratic function is (4,8). It means the point (4,8) will satisfy the function.
Substituting x=4 and P(x)=8 in (i).
[tex]8=a(4-2)(4-6)[/tex]
[tex]8=a(2)(-2)[/tex]
[tex]8=-4a[/tex]
Divide both sides by -4.
[tex]\dfrac{8}{-4}=a[/tex]
[tex]-2=a[/tex]
Putting [tex]a=-2[/tex] in (i), we get
[tex]P(x)=-2(x-2)(x-6)[/tex]
[tex]P(x)=-2(x^2-6x-2x+12)[/tex]
[tex]P(x)=-2(x^2-8x+12)[/tex]
[tex]P(x)=-2x^2+16x-24[/tex]
Therefore, the correct option is B.
can someone please explain how to complete this thanks
Help me ASAP please
Answer:
f(x) = x³ - 3
Step-by-step explanation:
Given f(x) then the graph of f(x) + c represents a vertical translation of f(x)
• If c > 0 then a shift up of c units
• If c < o then a shift down o c units
Here a shift down of 3 units, hence c = - 3, thus
f(x) = x³ - 3
just need number 5 !
Answer:
6.5
Step-by-step explanation:
Cos = Adjacent/Hypotenuse
For the angle with the measure of 70°
Adjacent = x
Hypotenuse = 19
Hence, cos 70 = x/19
multiply both sides by 19
cos(70) * 19 = 19cos(70)
x/19 * 19 = x
we're left with x = 19cos(70)
19cos(70) = 6.5 ( rounded to the nearest tenth )
x = 6.5
I hope this is help full to u
thank you
What congruent postulate is needed for these triangles
Answer:
i hope this helps you
Step-by-step explanation:
answer is c
REAL ASNWER ON THIS PLEASE
Answer:
240 degrees
Step-by-step explanation:
360 - 120 = 240
Answer:
240° i think
En un triangulo rectangulo,la hipotenusa mide 10 cm y un cateto mide 8 ¿Cual es el valor del otro cateto ?
Respuesta:
6 cm
Explicación paso a paso:
Paso 1: Información provista
Longitud de la hipotenusa (h): 10 cm
Longitud del cateto 1 (c₁): 8 cm
Paso 2: Calcular la longitud del cateto 2 (c₂)
Tenemos un triángulo rectángulo, es decir, que uno de sus ángulos es 90°. Conociendo la hipotenusa y uno de los catetos, podemos determinar la longitud del otro cateto usando el Teorema de Pitágoras.
h² = c₁² + c₂²
c₂² = h² - c₁²
c₂ = √(h² - c₁²)
c₂ = √((10 cm)² - (8 cm)²) = 6 cm
standard form, degree, leading coefficient of 2x(2)-7x(4)+5x
What is the slope of the line that passes through the points (-4,-4) and (-4,9)? Write answer in simplest form and explain how you got it.
(Answer as soon as you can please)
Factorize: (a+b)^2 + 4 (a+b)+ 4
What could be the coordinates of the third vertex, z, of triangle xyz so that it would have a hypotenuse with a length of square root 45 units
Answer:
[tex]z = (6,-1)[/tex]
Step-by-step explanation:
The missing parameters are:
[tex]x = (3,-1)[/tex]
[tex]y = (3,5)[/tex]
[tex]yz= \sqrt{45[/tex] --- Hypotenuse
Required
The coordinate of Z
First, calculate the distance xy
[tex]xy = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
[tex]xy = \sqrt{(3 - 3)^2 + (-1 - 5)^2}[/tex]
[tex]xy = \sqrt{0 + 36}[/tex]
[tex]xy = \sqrt{36}[/tex]
[tex]xy = 6[/tex]
By Pythagoras theorem, distance xz is:
[tex]yz^2 = xz^2 + xy^2[/tex]
[tex](\sqrt 45)^2 = xz^2 + 6^2[/tex]
[tex]45 = xz^2 + 36[/tex]
Collect like terms
[tex]xz^2 =45-36[/tex]
[tex]xz^2 =9[/tex]
[tex]xz = \sqrt{9}[/tex]
[tex]xz = 3[/tex]
This means that z is 3 units to the right of x
We have:
[tex]x = (3,-1)[/tex]
The rule to determine z is:
[tex](x,y) \to (x + 3, y)[/tex]
So, we have:
[tex]z = (3 + 3,-1)[/tex]
[tex]z = (6,-1)[/tex]
What do these terms represent? -8,-4, 0, 4, 8, 12
Answer:
They represent positive and negative numbers.
Step-by-step explanation:
HELPPPPP PLEASE !!!!!
Answer:
4th option 0,5,10,15
Step-by-step explanation:
Let's check if the first choice is geometric.
2*3 = 6. is 6*3 = 18, yes! is 18*3 = 54. Yep! its geometric
the second option multiplies by -2, it is geometric
the third option multiplies by 1/5, it is geometric
The fourth option does not multiply by anything common, it is Not geometric
Answer:
0,5,10,15 is not the sequence of geometric.
Generally, to check whether a given sequence is geometric, one simply checks whether successive entries in the sequence all have the same ratio. The common ratio of a geometric series may be negative, resulting in an alternating sequence.
Step-by-step explanation:
This is totally correct!
Selma uses a jogging trail that runs through a park near her home. The trail is a loop that is of a mile long. On Monday, Selma ran the loop in of an hour. What is Selma's unit rate in miles per hour for Monday's run?
Answer:
4.5 miles per hour
Step-by-step explanation:
Selma uses a jogging trail that runs through a park near her home. The trail is a loop that is 3/4 of a mile long. On Monday, Selma ran the loop in 1/6 of an hour. What is Selma's unit rate in miles per hour for Monday's run?
Distance = 3/4 of a mile
Time taken on Monday = 1/6 of an hour.
What is Selma's unit rate in miles per hour for Monday's run?
Unit rate in miles per hour for Monday's run = distance ÷ time taken
= 3/4 ÷ 1/6
= 3/4 × 6/1
= (3 * 6) / (4 * 1)
= 18/4
= 4.5 miles per hour
Unit rate in miles per hour for Monday's run = 4.5 miles per hour
Elsa uses exactly 60 cubes of ice to build a rectangular ice prism. Each cube has side lengths of 1 unit. Enter the dimensions of the rectangular ice prism below assuming that none of the sides can have a length of 10 units. Your answer should be typed like this with the numbers going from smallest to largest: 1, 2, 3 *
Answer:
2, 5, 6
Step-by-step explanation:
The volume of a rectangular prism is given by [tex]V=l\cdot w\cdot h[/tex], where all variables to the right are dimensions of the prism.
Therefore, we're looking for three numbers that multiply to be 60.
Since the question stipulates that no side length may be 10, we have:
[tex]2\cdot 5\cdot 6=60[/tex]
Tell whether the points appear to represent a linear function, an exponential function, or neither? Explain please.
Answer:
Exponential
Step-by-step explanation:
Linear is easy to remember because it goes in a straight LINE.
Only other option is a quadratic and this does not create a parabola
Yani buys 4 dozen flyers for $7.80. What is the unit rate?
Answer:
The unit rate is, $1.95
Step-by-step explanation:
7.80 ÷ 4= 1.95
So , unit rate is [tex]\frac{1}{1.95\\}[/tex]
ANSWER THIS PLEASE IT IS A MATH QUESTION
Answer:
Step-by-step explanation:
Least to largest:
First compare the whole parts of the decimal number. The whole part with greater number will be the greatest number.
2) Then compare the decimal parts. Compare tenth place. The decimal number that has greater number in the tenth place will be greater.
3) If the number in tenth place is equal, then compare 100th place and so on
A) 15.99 ; 16 ; 16.02 ; 16.2
B) 4.45 ; 4.9945 ; 5.545 ; 5.56
c) 44.11 ; 44.5 ; 45 ; 45.01
D) 8.995 ; 9.0599 ; 9.27 ; 9.6
Greatest to least
A) 2.111 ; 2.11 ; 2.1 ; 2.01
B) 32.32 ; 32.302 ; 32.032 ; 3.99
c) 7.666 ; 7.66 ; 7.6 ; 7.06
D) 57.68 ; 57.57 ; 57.057 ; 5.75
please help with this problem !!
Answer:
a. x= 9
b. 70
c. 110
d. 70
e. 110
Step-by-step explanation:
a.
congruent angles have the same measure. 1 and 3 are congruent and 2 and 4 are congruent
2(12x+2)+2(7x+7)=360
divide both sides by 2
12x+2+7x+7=180
combine like terms
2+7=9
12x+7x=19x
19x+9=180
subtract both sides by 9
19x=171
divide both sides by 19
x=9
7x+7,
7*9+7
63+7 = 70
1 is 70, 3 is 70
12x+2, x=9
108+2 = 110
2 and 4 is 110
Answer:
Step-by-step explanation:
Angles 1 and 2 are supplementary (their sum is 180 degrees)
7x + 7 + 12x + 2 = 180
19x= 171
x = 9
m 1 = 7 * 9 + 7 = 70 degrees
m 2 = 12 * 9 + 2 = 108 + 2 = 110 degrees
m 3 = angle 1 and angle 3 are vertical, so they have the same measure: 70 degrees.
m 4 = angle 2 and angle 4 have the same measure: 110 degrees
Which relationship has a zero slope?
a²+b²=c²
5²+9²=c²
25²+81²=c²
106=c²10.2
5
line a is perpendicular to B.
if the slope of line A is -3/4 what is the line of B
Step-by-step explanation:
line a is perpendicular to B.
if the slope of line A is -3/4 what is the line of B
find the measure of
Answer:
46°
Step-by-step explanation:
D = 90° - 44° = 46°
The cost to rent a moving truck is a flat fee of $25 plus $0.60 per mile. The equatic
c, in dollars for the number of miles, m, traveled in the truck.
Identify the independent and dependent variables.
The
is the independent variable.
The
is the dependent variable.
$25 flat fee
cost
miles traveled?
Answer:
See explanation below
Step-by-step explanation:
Flat fee = $25
Cost per mile = $0.60
Let
C = total cost
m = number of miles travelled by the truck
The equation is
C = 25 + 0.60m
The independent variable is miles,m travelled
The dependent variable is total cost, C
$25 is the constant
which is the best estimate for the percentage equivalent of 7/15
Answer:
45%
Step-by-step explanation:
State one obtuse angle and one acute angle
Answer:
obtuse angle is 2 and acute angle is 1
Step-by-step explanation:
Obtuse Angle: An angle between 90 and 180 so angle 2 is an obtuse angle
Acute Angle: An angle between 0 and 90 so angle 1 is an acute angle
Find the volume of the prism. 5 cm 13 cm 13 cm
Hey guys, I need help with this question. Please show working out, thanks
Answer:
Step-by-step explanation:
In similar triangles corresponding triangles are in same ratio.
[tex]\frac{15}{5}=\frac{12}{y}[/tex]
Cross multiply,
15 * y = 12 * 5
y = [tex]\frac{12*5}{15}[/tex]
y = 4
Need help quick it's urgent!
please help with 3 , 4 & 5 i mark Brian list
Answer:
see belowStep-by-step explanation:
Question-2:the square of x-5 given by
[tex] \displaystyle (x - 5) ^{2} [/tex]
use (a-b)²=a²-2ab+b² to simplify so we obtain:
[tex] \displaystyle {x}^{2} - 10x + 25[/tex]
hence
our answer is 2)
Question-3:to find:
[tex]f(x) - g(x)[/tex]
substitute the value of f(x) and g(x):
[tex] \rm \displaystyle{6x}^{2} + 8x - 5 - ( {2x}^{2} - 4x + 4)[/tex]
remove parentheses and change its sign:
[tex] \rm \displaystyle{6x}^{2} + 8x - 5 - {2x}^{2} + 4x - 4[/tex]
combine like terms:
[tex] \rm \displaystyle{6x}^{2} + 12x - 5 - {2x}^{2} - 4[/tex]
collect like terms:
[tex] \rm \displaystyle{4x}^{2} + 12x -9[/tex]
hence,
our answer is 3)
Question-4:given Polynomial:
[tex] \displaystyle {5x}^{3} + 2 {x}^{2} + 7[/tex]
substitute the value of x:
[tex] \displaystyle {5.(10}^{3}) + 2 ({10}^{2}) + 7[/tex]
simplify squares:
[tex] \displaystyle 5(1000) + 2 (100) + 7[/tex]
simplify multiplication:
[tex] \displaystyle 5000 + 2 00 + 7[/tex]
simplify addition:
[tex] \displaystyle 5207 [/tex]
hence our answer is 1)
Question-5:given:
12x³y⁶,8x⁴y,20x²y⁵notice that,
every time there's a GCF of 4x²y
hence our answer is 4)
HELP ME BEFORE I DIE!
Your adjacent is 3, your opposite is 4, and you have a 90 degree angle. Find the value of cos V rounded to the nearest hundredth, if necessary.
Answer:
0.6 or [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
Using the Pythagorean theorem ([tex]a^{2} +b^{2} =c^{2}[/tex]) we get that the hypotenuse is 5.
so the cos V is adjacent over the hypotenuse. so if adjacent is 3 and hypotenuse is 5, the answer is [tex]\frac{3}{5}[/tex] which equals 0.6 in decimal form.
Stacy invited six friends to her 5th birthday party. How many ways can Stacy's mom arrange the
children around the table for cupcakes and ice cream?
(Answer with no decimals)
Answer:
120 ways
Step-by-step explanation:
Here, we are looking at arranging around a table
To do this, we sit down one of the children and arrange the remaining around the one that we have sat down
In scenario like this, the number of possible arrangement ways will be;
(n-1)! ways
where n is the number of children which is 6 in this case
So the possible number of ways will be;
(6-1)! = 5! = 120 ways