The quadratic parent function has been reflected down, stretched vertically by a factor of 1/3, shifted vertically by 9 units and shifted horizontally by -12 units.
1a) write the function g(x) in vertex form
1b) then rewrite the vertex form into standard form
Answer:
1a) f(x) = -1/3(x + 12)² + 9
1b) f(x) = -1/3x² - 8x - 39
General Formulas and Concepts:
Algebra I
Equality Properties
Expand by FOIL (First Outside Inside Last)
Standard Form: ax² + bx + c = 0
Transformations Graph: f(x) = a(bx - c)² + d
a = vertical shrink/stretch b = horizontal shrink/stretch c = horizontal movement left/right d = vertical movement up/downStep-by-step explanation:
Step 1: Define
Reflected down and vertically stretched by 1/3: a = -1/3
Shifted vertically by 9 units: d = 9
Shifted horizontally by -12 units: c = -12
Step 2: Write Vertex Form
Define: f(x) = a(bx - c)² + d Substitute: f(x) = -1/3(x + 12)² + 9Step 3: Write Standard Form
Define: f(x) = -1/3(x + 12)² + 9Expand: f(x) = -1/3(x² + 24x + 144) + 9Distribute -1/3: f(x) = -1/3x² - 8x - 48 + 9Combine like terms: f(x) = -1/3x² - 8x - 39And we have our final answers!
A recipe for biscuits says to mix 6 cups of flour with 2 cups of milk. How many cups of flour would you need for 3 cups of milk?
Answer:
9 cups of flour
Step-by-step explanation:
6 / 2 = 3
3 • 3 = 9
1 3/4 divided by 1/2-1 1/2 to the 3rd
Answer:
-7/4
1/8
Step-by-step explanation:
1. If the problem is; (1 3/4) / (1/2 - 1 1/2)^(3)
(a). Convert to improper fractions;
(7/4) / (1/2 - 3/2)^3
(b). Simplify;
(7/4) / (-2/2)^3
(7/4) / (-1)^3
(7/4) / (-1)
-7/4
2. If the problem is; ((1 3/4) / (1/2)) - (1 1/2)^3
(a). Convert to improper fractions;
((7/4)/ (1/2)) - (3/2)^3
(b). Simplify;
((7/4)/ (1/2)) - (3/2)^3
((7/4)*(2/1)) - (27/8)
(7/2) - (27/8)
(28/8) - (27/8)
1/8
Find the area of the figure shown below. Use 3.14 for π and round your answer to the nearest hundredth.
Answer:
ans: 111.54
Step-by-step explanation:
u can simple do by multiple
Answer:
38.24
Step-by-step explanation:
arrangement the following in ascending order ; -5/7, -3/14, 4/7, -6/7
Answer:
-4/7-5/7-6/7-3/14 ascending order
Answer:
The sorted inputs in order from least to greatest is:
-6/7 < -5/7 < -3/14 < 4/7
Step-by-step explanation:
Given
-5/7, -3/14, 4/7, -6/7
The least common denominator (LCD) is: 14
Rewriting as equivalent fractions with the LCD:
-5/7 -3/14 4/7 -6/7
-10/14 -3/14 8/14 -12/14
Sorting this table by the numerators of the equivalent fractions in order from least to greatest:
-6/7 -5/7 -3/14 4/7
-12/14 < -10/14 < -3/14 < 8/14
Therefore, the sorted inputs in order from least to greatest is:
-6/7 < -5/7 < -3/14 < 4/7
FInd the circumference of a circle with a diameter of 6 yd. Use the value 3.14 for x and do not round your answers
Answer:
C ≈ 18.85yd
Step-by-step explanation:
15 kg equals how many grams
Answer:
15,000g
Step-by-step explanation:
Answer: 15000 grams
Step-by-step explanation: To convert Kilograms to Grams, you'll need to multiply the mass value by 1000.
Answer the two questions below. THANKS!!
Problem 1
We're given that angle A = angle B. Also that angle B = angle C.
By the transitive property, we can say angle A = angle C.
So basically all three angles are equal to one another. Let's call that unknown angle x.
For any triangle, the three angles always add to 180, so,
x+x+x = 180
3x = 180
x = 180/3
x = 60
That proves angles A,B, and C are each 60 degrees. This triangle is considered equiangular since all angles are the same. Furthermore, the triangle is also considered equilateral meaning all sides are the same. The term equilateral is more widely used, so I'd go with that term if you could only pick one.
==========================================================
Problem 2
As mentioned in problem 1, the three angles of a triangle add to 180
A+B+C = 180
A+B+90 = 180
A+B+90-90 = 180-90
A+B = 90
This shows A and B are complementary angles. Complementary angles by definition add to 90 degrees.
what is the answer of CGF of 9 and 12
Answer:
The answer of CGF is 3.................
Answer:
3
Step-by-step explanation:
List the factors of each number
factors of 9 are 1, 3, 9
factors of 12 are 1, 2, 3, 4, 6, 12
The common factors are 1 and 3
GCF = 3
The value of a ratio is __________.
the sum of the two quantities in the ratio
the quotient of the two quantities in the ratio
the difference of the two quantities in the ratio
the product of the two quantities in the ratio
Answer:
B.
Step-by-step explanation: The value of a ratio is the quotient of the two quantities in the ratio.
Answer:
B
the quotient of the two quantities in the ratio
johnny invests $9000 in two mutual funds
Answer:
$4500 each if he splits it eqaully
Step-by-step explanation:
9000÷2=4500
hope this helped (~‾▿‾)~
.............llllllllllllllllwwwwwwww
Answer:
wwwwwwwwwwwwwwwwwww
a=4, b = 5, A = 16
Solve the Triangle
Triangle has two solutions: a=4; b=5; c=1.051 and a=4; b=5; c=8.561.
Extra: #1 Obtuse scalene triangle.
Sides: a = 4 b = 5 c = 1.051
Area: T = 0.724
Perimeter: p = 10.051
Semiperimeter: s = 5.026
Angle ∠ A = α = 16° = 0.279 rad
Angle ∠ B = β = 159.846° = 159°50'45″ = 2.79 rad
Angle ∠ C = γ = 4.154° = 4°9'15″ = 0.073 rad
Height: ha = 0.362
Height: hb = 0.29
Height: hc = 1.378
Median: ma = 3.009
Median: mb = 1.517
Median: mc = 4.497
Inradius: r = 0.144
Circumradius: R = 7.256
Vertex coordinates: A[1.051; 0] B[0; 0] C[-3.755; 1.378]
Centroid: CG[-0.901; 0.459]
Coordinates of the circumscribed circle: U[0.526; 7.237]
Coordinates of the inscribed circle: I[0.026; 0.144]
Exterior (or external, outer) angles of the triangle:
∠ A' = α' = 164° = 0.279 rad
∠ B' = β' = 20.154° = 20°9'15″ = 2.79 rad
∠ C' = γ' = 175.846° = 175°50'45″ = 0.073 rad
If a farmer is able to get 120 eggs from 20 chickens, how many eggs is the farmer able to get per chicken?
Answer:
6 eggs per chicken
Step-by-step explanation:
hdjdjidbdudbddjow0s
Answer:
6
Step-by-step explanation:
1 point
The weights of laboratory cockroaches follow a Normal distribution with
mean 80 grams and standard deviation 2 grams. Use the figure from above.
About what percent of the cockroaches have weights less than 78 grams?
16%
none of these
32%
34%
O 2.5%
Answer:
16% of the cockroaches have weights less than 78 grams.
Option A is correct.
Step-by-step explanation:
Mean = 80 g
Standard Deviation = 2
We need to find percent of the cockroaches have weights less than 78 grams so, x=78
First we will find z using formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Putting values of x, mean and Standard Deviation to find z
[tex]z=\frac{x-\mu}{\sigma}\\z=\frac{78-80}{2}\\z=-1[/tex]
We need to find P(z<-1)
Looking in the normal distribution table
[tex]P(z<-1)=0.15866\\P(z<-1)\approx 0.16\\Converting \ into \ percentage\\P(z<-1)=16\%[/tex]
So, 16% of the cockroaches have weights less than 78 grams.
Option A is correct.
Which fact helps you prove the isosceles triangle theorem, which states that the base angles of any isosceles triangle have equal measure? The base angles of an equilateral triangle have equal measure. If two sides of a triangle are equal, the third side must be equal to the others. If a triangle is equiangular, then it is equilateral. If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle.
Answer:
If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle.
The fact which helps to prove the isosceles theorem is; The base angles of an equilateral triangle have equal measure.
Isoscelles triangleIsoscelles triangles in plane shape concept are characterized by two equal sides.
On this note, similarly in equilateral triangles, 2 sides are equal ( although, all sides of an equilateral triangle are equal).
Ultimately, the statement which helps to prove the isosceles triangle theorem is therefore; The base angles of an equilateral triangle have equal measure since all the two sides are equal as in isoscelles triangles too.
Read more on isoscelles triangle;
https://brainly.com/question/11884412
complete the statements,extra points!!! please don't answer if you don't know
Answer:
1. 0.08703 killograms
2. Decameters
3. Liters
Step-by-step explanation:
convert.
1. Eight people work in an office. They are paid hourly rates of 12£,15£,15£,14£,14£,13£,14£,13£
(a) Find: (i) the mean (ii) the median (iii) the mode.
Which of these is equivalent to 3/8 x 5/6 Answer Correctly Or Dont Answer
A. 15/4
B. 16/5
C. 8/14
D. 8/48
What is the unit price of 6 pounds of chocolate that costs $51.00?
Answer:
$8.50 per pound
Step-by-step explanation:
51/6=8.5
The price of 1 pound is $8.5
What is an Equation ?An equation is a statement that relates expressions with constants or another expressions.
It is given that
6 pounds of chocolate costs $51
then let 1 pound of chocolate costs $x
The equation formed will be
x = $51/6 = $8.5
Therefore the price of 1 pound is $8.5
To know more about Equation
https://brainly.com/question/10413253
#SPJ2
plz help................
Answer:
Step-by-step explanation:
1,2222
2,3333
3,4444
4,5555
5,6666
6,7777
7,8888
8,9999
9,10101010
Give the factors for the numerator [n] and denominator [d] after reducing.
Answer:
The factors for the numerator [n] and denominator [d] after reducing will be:
[tex]\frac{x^2-25}{x^2-4x}\div \:\frac{2x^2+2x-40}{x^3-x}=\frac{\left(x-5\right)\left(x+1\right)\left(x-1\right)}{2\left(x-4\right)^2}[/tex]
Step-by-step explanation:
Given the expression
[tex]\frac{x^2-25}{x^2-4x}\div \frac{2x^2+2x-40}{x^3-x}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}[/tex]
[tex]=\frac{x^2-25}{x^2-4x}\times \frac{x^3-x}{2x^2+2x-40}[/tex]
[tex]\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}[/tex]
[tex]=\frac{\left(x^2-25\right)\left(x^3-x\right)}{\left(x^2-4x\right)\left(2x^2+2x-40\right)}[/tex]
[tex]=\frac{\left(x^2-25\right)x\left(x^2-1\right)}{\left(x^2-4x\right)\left(2x^2+2x-40\right)}[/tex]
[tex]\mathrm{Cancel\:the\:common\:factor:}\:x[/tex]
[tex]=\frac{\left(x^2-25\right)\left(x^2-1\right)}{2\left(x-4\right)\left(x^2+x-20\right)}[/tex]
∵ As factor [tex]\left(x^2-25\right)\left(x^2-1\right)=\left(x+5\right)\left(x-5\right)\left(x+1\right)\left(x-1\right)[/tex]
so the expression becomes
[tex]=\frac{\left(x+5\right)\left(x-5\right)\left(x+1\right)\left(x-1\right)}{2\left(x-4\right)\left(x^2+x-20\right)}[/tex]
∵ As factor [tex]2\left(x-4\right)\left(x^2+x-20\right)=2\left(x-4\right)^2\left(x+5\right)[/tex]
so the expression becomes
[tex]=\frac{\left(x+5\right)\left(x-5\right)\left(x+1\right)\left(x-1\right)}{2\left(x-4\right)^2\left(x+5\right)}[/tex]
[tex]\mathrm{Cancel\:the\:common\:factor:}\:x+5[/tex]
[tex]=\frac{\left(x-5\right)\left(x+1\right)\left(x-1\right)}{2\left(x-4\right)^2}[/tex]
Therefore, the factors for the numerator [n] and denominator [d] after reducing will be:
[tex]\frac{x^2-25}{x^2-4x}\div \:\frac{2x^2+2x-40}{x^3-x}=\frac{\left(x-5\right)\left(x+1\right)\left(x-1\right)}{2\left(x-4\right)^2}[/tex]
A large bottle of orange juice contains 400 mL of juice. A medium size bottle contains 60% as much. Find how many millilters are in the medium bottle using the double number line.
Answer:
240 mL
Step-by-step explanation:
60% of 400 is 240 mL! Your Welcome!
Answer:
the answer would be 240
Step-by-step explanation:
you have to take the percentage and turn it into a decimal by dividing by 100 and that gets you .6 and then you have to time 400 by .6 and then you get your answer
Write the slope-intercept form of the equation of the line described. Through (-2, -2) parallel to y = -2/7x -5
Answer: y= -2/7x-2
Step-by-step explanation:
To be parrell they have to have the same slope but different y intercepts.
so just put -2 so it will cross that point
A middle school took all of its 6th grade students on a field trip to see a symphony at a theater that has 2500 seats. The students filled 66% of the seats in the theater. How many 6th graders went on the trip?
Answer:
1650
Step-by-step explanation:
66% = 66/100
66/100 times 2500 = 0.66 times 2500 = 1650
There were 1650 students
the perimeter of a triangle is
88 centimeters. If two sides are equally long and the third side is
7 centimeters longer than the others, find the lengths of the three sides.
please answer as fast as possible see image
Answer:
388
Step-by-step explanation:
We need to find the area of the semicircle and parallelogram separately and then combine.
The formula for the area of a semicircle is 1/2(pi*r^2)
r = 12. 12^2 = 144
1/2(pi*144) = 226..1946711 which we can just round to 226
The formula for the area of a parallelogram is bh
b = 18, h = 9. 18*9 = 162.
226+162 = 388
Answer:
218.55Step-by-step explanation:
total area = semi circle + parallelogram
= (1/2 π 6²) + (9 x 18)
= 56.55 + 162
= 218.55 sq. units
Which graph shows different numbers of gold coins that colin can find go win more than 200 points?
Answer:
Step-by-step explanation:
Its the closed dot on 9. i just did the quiz. Your welcome.
Answer: the closed dots on 9 10 11 12 13 14
15
List or circle the possible values that satisfy each inequality.
First question: 5, 10
Second question: 2, 3, 5
To solve this, plug each of the numbers into the inequality and circle the numbers that make the inequality true.
Match each equation on the left to the mathematical property it uses on the right.
Answer: 1,d 2,e 3,c 4,b 5,a
Step-by-step explanation:
Number is from top to bottom on left and letters are same way on right.