The vertex form of a quadratic function is f(x) = a(x - h)2 + k. What is the vertex of each function? Match the function rule with the coordinates of its vertex.
Answers
Answer:
For [tex]f(x)=6(x-5)^2-9[/tex] the vertex is: (5, -9)
For [tex]f(x)=9(x+5)^2-6[/tex] the vertex is: (-5, -6)
For [tex]f(x)=5(x-6)^2+9[/tex] the vertex is: (6, 9)
For [tex]f(x)=6(x+9)^2-5[/tex] the vertex is: (-9, -5)
For [tex]f(x)=9(x-5)^2+6[/tex] the vertex is: (5, 6)
Step-by-step explanation:
Let's identify the vertex pair [tex](x_v,y_v)[/tex] from each equation:
A) [tex]f(x)=6(x-5)^2-9[/tex] corresponds to [tex]x_v=5\,\,\,and\,\,\,y_v=-9[/tex] , that is: (5, -9)
B) [tex]f(x)=9(x+5)^2-6[/tex] corresponds to [tex]x_v=-5\,\,\,and\,\,\,y_v=-6[/tex] , that is: (-5, -6)
C) [tex]f(x)=5(x-6)^2+9[/tex] corresponds to [tex]x_v=6\,\,\,and\,\,\,y_v=9[/tex] , that is: (6, 9)
D) [tex]f(x)=6(x+9)^2-5[/tex] corresponds to [tex]x_v=-9\,\,\,and\,\,\,y_v=-5[/tex] , that is: (-9, -5)
E) [tex]f(x)=9(x-5)^2+6[/tex] corresponds to [tex]x_v=5\,\,\,and\,\,\,y_v=6[/tex] , that is: (5, 6)
Related Questions
Which represents where f(x) = g(x)?
f(2) = 9(2) and f(0) = g(0)
f(2) = g(0) and f(0) = g(4)
f(2) = g(0) and f(4) = g(2)
of(2) = g(4) and f(1) = g(1)
Answers
Answer:g
2
Step-by-step explanation:the is answer is by the multiply the numbers
Find the distance between these points.
R(-1, 0), S (8, 6)
√(26)
√(85)
3√(13)
Answers
Answer:
3√13
Step-by-step explanation:
Distance = (-1,0) (8,6) =3√13
1: The distance between (-1,0) (8,6) is= √8-(-1))2+(6-0)2 = 3√13
Answer: 3√13
Hope this helps.
Solve the equation using square roots.
[tex]4x^{2} +9=0[/tex]
Answers
Isolating the variable terms and dividing by 4, we have [tex]x^2=-\frac{9}{4}.[/tex] Taking the square root, we have [tex]\boxed{x=\frac{3i}{2},-\frac{3i}{2}}.[/tex]
one over four times x is equal to -2. What is x?
Answers
Answer:
x = -8
Step-by-step explanation:
Step 1: Write the equation
1/4x = -2
Step 2: Divide both sides by 1/4
You should get -8 as your final answer.
Answer:
x = -8
Step-by-step explanation:
1/4 x = -2
Multiply each side by 4
1/4 x * 4 = -2*4
x = -8
The area of a rectangle is equal to its length times its width. If the area of a rectangle
is 14x + 42 square feet, which option(s) could be the length and width of that rectangle?
Answers
Answer:
one option could be : 7x+21 and 2
Create an inequality that represents the verbal description below.
The product of ten and a number is greater than the difference of four times the number and two.
Answers
Answer:
10*x > 4x-2
Step-by-step explanation:
Following the instructions we get the above inequality.
Answer:
10x > 4-2
Step-by-step explanation:
Can someone please help me with this
Answers
Answer:
The second one. -0,55 > -0.8
Step-by-step explanation:
The point in the right is -0.55, the other one (left) is -0.8. -0.55 is greater than -0.8.
A circular garden has a diameter of 6 feet. There are 2 sections of blue flowers and 1 section of white flowers as shown. What is the area of the section with the white flowers?
Answers
Answer:
[tex]( Exactly ) 5.25\pi[/tex]
Step-by-step explanation:
[tex]See Attachment Below;[/tex]
Write the equation of a line that passes through (1,9) and has a slope of -3, please!
Answers
Answer:
y = -3x + 12
Step-by-step explanation:
Very similar to the other question i answered, by here's a step by step anyway in case you find it helpful : )
There are lots of different methods to do these types of questions, but this is the way i like to do it.
Coordinate (x1, y1) : (1, 9) and Gradient (m): -3
Start with this generic equation:
y- y1 = m(x-x1)
Substitute in the values they have given you:
y - (9) = -3(x-1)
This becomes:
y -9 = -3x +3
Keep solving by moving the 10 over to the other side:
y = -3x + 3 +9
y = -3x + 12
An easy way to double check:
1) the coefficient of x is the slope. We got -3x, and the slope is -3, so that's correct.
2) Substitute x=1 into the equation, and we get 9, which is the exact coordinate that they gave us. This is also right.
Hope this helped : )
Explain how to find the other leg if the hypotenuse is 25cm and one leg measures 7 cm.
Answers
______________________________
The other leg equals 24 cm
please see the attached picture for full solution
Hope it helps
Good luck on your assignment
___________________________.
What angle has the same sine value between 0-180? as Sin 24
A Sine 156
B Sine 123
C Sine 145
D Sine 154
Answers
Answer:
[tex]Sin156[/tex]
Step-by-step explanation:
Given
[tex]Sin24[/tex]
Required
Find equivalent between 0 to 180;
Let 24 be represented by [tex]\theta[/tex]
So, [tex]\theta = 24[/tex]
From Trigonometry ratios;
[tex]Sin\theta = Sin(180 - \theta)[/tex] where [tex]0\leq \theta \leq 180[/tex]
Recall that [tex]\theta = 24[/tex]
So, we have to substitute 24 for [tex]\theta[/tex] in the above expression.
This gives
[tex]Sin24= Sin(180 - 24)[/tex]
Subtract 24 from 180
[tex]Sin24= Sin156[/tex]
Hence, the equivalent of [tex]Sin24[/tex] is [tex]Sin156[/tex]
what is the base plan for the set of stacked cubes?
Answers
Answer:
i think it is the 3 one from the left side
Step-by-step explanation:
Find two mixed numbers or fractions with a quotient of 3.2
Answers
Answer:
[tex]\frac{32}{10}\\\\\frac{64}{20}\\\\\frac{96}{30}[/tex]
These all thave the same quotient of 3.2
Step-by-step explanation:
The fractions which are given and and which are also required are called equivalent fraction. In this, the denominator and numerator of both fractions is different, but when you divide the numerator and denominator to get a value, the values of both the fractions are found same.
To find 2 mixed number or fraction with a quotient 3.2.
We can write 3.2 in the fractional form:
[tex]3.2 = \frac{32}{10}[/tex]
Now multiply both the numerator and denominator with 2, we get
[tex]\frac{2\cdot32}{2\cdot10}= \frac{64}{20}[/tex]
which also has the quotient 3.2
Similarly, multiply both numerator and denominator of 32/10 by 3, we get
[tex]\frac{3\cdot32}{3\cdot10}=\frac{96}{10}[/tex]
whici also has the quotient of 3.2
Similarly we can go on to find as many values as we want with the same quotient.
What is the Lowest Common Denominator between 3m/m+n and 3n/m-n
Answers
Answer:
Step-by-step explanation:
Denominators (m +n) & (m- n) doesn't have any common factors.
So to find the lowest common denominator, multiply them
LCD = (m+n) (m-n)
4(7x-1)=3(2x+1)-4(x+6) plzz help
Answers
Answer:
[tex]x=-\dfrac{17}{26}[/tex]
Step-by-step explanation:
[tex]4(7x-1)=3(2x+1)-4(x+6)[/tex]
Expand parentheses:
[tex]28x-4=6x+3-4x-24[/tex]
Combine like terms:
[tex]28x-4=2x-21[/tex]
Subtract 2x from both sides:
[tex]26x-4=-21[/tex]
Add 4 to both sides:
[tex]26x=-17[/tex]
Divide both sides by 26:
[tex]x=-\dfrac{17}{26}[/tex]
Hope this helps!
Answer:
[tex]x = \frac{ - 17}{26} \\ \\ [/tex]
Step-by-step explanation:
[tex]4(7x - 1) = 3(2x + 1) - 4(x + 6) \\ 28x - 4 = 6x + 3 - 4x - 24 \\ 28x - 6x + 4x = 4 + 3 - 24 \\ 26x = - 17\\ \frac{26x}{26} = \frac{ - 17}{26} \\ x = \frac{ - 17}{26} \\ [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Solve the system of equations:
y = 2x – 2
y = x2 – x – 6
A. (–2, 0) and (3, 0)
B. (–1, –5) and (4, 2)
C. (–1, –4) and (4, 6)
D. (0, –2) and (2, 2)
Answers
Answer: C. (-1, -4) and (4, 6)
Step-by-step explanation:
FACTOR
h² + 9hj + 14j²
Answers
Answer:
(h+7j)*(h+2j)
Step-by-step explanation:
h^2+7hj+2hj+14j^2
h*(h+7j)+2j*(h+7j)=(h+7j)*(h+2j)
So the right answer is (h+2)(h+7j)
please see attached picture for full solution
Hope it helps
Good luck on your assignment
Stay safe
For what values of x and y are the triangles to the right congruent by HL?
Answers
Work must be shown for this problem! The figure shown below is a rectangle. Give the angle value (numerical, not the letters).
Answers
Answer:
58 degrees
Step-by-step explanation:
In a rectangle, the two diagonals form four isosceles triangles. This means triangle EBC is isosceles. In an isosceles triangle, the two base angles are the same. So, angles EBC and BCE are both 61. Now, in a triangle, the three angles add up to 180. So, 61+61=122, and to find angle CEB you need to subtract 180-122. 180-122=58 degrees.
Answer:
58°
Step-by-step explanation:
to find m∠CEB
triangle CEB is formed by the two parts of rectangle diagonals (and BC), and as we know, diagonals bisect each other, thus EB is congruent to EC, and it is an isosceles triangle
We also know that angles opposite congruent sides are congruent, thus,
angles EBC and ECB are congruent
thus angle ECB= 61°
We know that the inner angle measures of a triangle according to Angle Sum Theorem add up to 180°
Thus,m angle EBC + m angle ECB + m angle CEB= 180
Now we know that both EBC and ECB are angles with the measure of 61 °, so lets put the measures in instead of angles into the equation
61+61+m angle CEB=180
122 + m angle CEB =180
m angle CEB=180-122
m angle CEB=58°
How do you answer the questions in the picture?? Please helppp!!
Answers
Answer:
a) 1.50 m/s²
b) 675m
c) 11.25 m/s
Step-by-step explanation:
1. a) Acceleration can be found from the gradient of a speed-time graph, which is the graph we have here.
Notice that the graph from t=0 to t=10 has the same gradient thoughout (since it is a straight line). Hence, the acceleration when t=4 is the same as the acceleration from t=0 to t=10.
To find the gradient of the graph from t=0 to t=10, use the gradient formula below:
gradient=[tex] \frac{y1 - y2}{x1 - x2} [/tex]
The coordinates of the point at t=0 is (0,0) and the point at t=10 is (10,15).
Thus, gradient
[tex] = \frac{15 - 0}{10 - 0} \\ = \frac{15}{10} \\ = 1.5[/tex]
Therefore the acceleration when t=4 is 1.50 m/s².
*Acceleration is the rate of change of velocity (or speed).
b) Distance travelled can be found by calculating the area under a speed-time graph.
The area under the graph is the orange trapezium that the question has shaded for you already.
Formula for area of trapezium= ½(a+b)(height)
a+b is the total length of the two parallel horizontal lines of the trapezium.
Let the top line be a and the bottom line be b.
length of a= distance between (10,15) and (40,15)
Length of a
= 40 -10
= 30 units
Length of b
= 60 -0
= 60 units
height of trapezium= 15 units
Area of trapezium
= ½(30 +60)(15)
= 675 units²
Thus, the distance travelled is 675m.
c) Avg speed= total distance ÷ total time
From part b, we know that the total distance travelled is 675m. The total time is 60s since the graph is from t=0 to t=60.
Hence, average speed
= 675 ÷60
= 11.25 m/s
Many individuals over the age of 40 develop intolerance for milk and milk-based products. A
dairy has developed a line of lactose-free products that are more tolerable to such individuals. To
assess the potential market for these products, the dairy commissioned a market research study of individuals over 40 years old in its sales area. A random sample of 250 individuals showed that 86 of them suffer from milk intolerance. Based on the sample results, calculate a 90% confidence
interval for the population proportion that suffers milk intolerance. Interpret this confidence interval.
a) First, show that it is okay to use the 1-proportion z-interval. (Assumptions)
b) calcuate by hand a 90% confidence interval (use the formula)
c) provide an interpretation (conclusion)
d) if the level of confidence was 95% instead of 90% would the resulting interval be narrower or wider? explain. (show your computation before your explanation)
e) if the researchers were interested in the 90% interval with the 3% margin of error what size sample would they require?
f) verify your 90% confidence interval using your calculator.
Answers
Answer:
p = 86/250 = 0.344
z_c = 1.65 at 90% confidence.
margin of error, E = sqrt(pq/n)*z_c
= sqrt(0.344*(1-0.344)/250)*1.65
= 0.0496
90% CI = (p -E , p + E)
= (0.344 - 0.0496 , 0.344 + 0.0496)
= (0.2944, 0.3936) (Ans.)
Step-by-step explanation:
PLS HELP RQ!!!!!!!!!!!!!11
Answers
Answer:
3 3/4 cubic inches
Step-by-step explanation:
2.5*1.5*1
Answer:
15 cubic inches
Step-by-step explanation:
Find the volume of the pyramid.
Answers
Answer:
The answer is 112 ft squared
Step-by-step explanation:
Which of these expressions can be used to calculate the monthly payment for
a 30-year loan for $190,000 at 11.4% interest, compounded monthly?
??
Answers
Answer:
$1,867.07 monthly payment
Step-by-step explanation:
1. Define variables to calculate the monthly payment for loans, using:
A = total loan amount (how much you borrow)
R = annual interest rate (in %)
N = number of payments per year
2. Use this formula to calculate monthly payment (M):
[tex]M = A* \frac{R}{N}[/tex]
3. Substitute variables with values from excercise as below (11.4% = 0.114):
[tex]M = 190000 * \frac{0.114}{12} = 1867.07[/tex]
4. The calculated result is a monthly payment installment in given currency (in this case $)
what is the surface area of the given figure?
Answers
The one-year survival rate for pancreatic cancer is 20%. Of 12 people diagnosed with pancreatic cancer at one hospital, 6 survived one year. What is the probability of that happening?
Answers
Answer:
50% if your looking at %
I’m stuck on this can someone help?
Answers
Answer:
13
Step-by-step explanation:
f(10)=10/2+8
f(10)=5+8
f(10)=13
Hey there!
Answer:
f(x) = 13 when x = 10.
Step-by-step explanation:
To find f(x) when x = 10, simply substitute '10' for 'x'.
[tex]f(x) = \frac{x}{2} + 8[/tex]
Subsitute in '10' for 'x':
[tex]f(10) = \frac{10}{2} + 8[/tex]
Simplify:
[tex]f(10) = 5 + 8[/tex]
[tex]f(10) = 13[/tex]
Therefore, f(x) = 13 when x = 10.
Noah says that 9x - 2x + 4x is equivalent to 3x, because the subtraction sign tells us to subtract everything that comes from after 9x. Elena says that 9x - 2x + 4x is equivalent to 11x, because the subtraction only applies to 2x. Do you agree with either of them? Explain ur reasoning. i
Answers
Agree with Elena, because 9x - 2x + 4x is equivalent to 11x, after the subtraction only applies to 2x.
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
Noah says that 9x - 2x + 4x is equivalent to 3x, because the subtraction sign tells us to subtract everything that comes from after 9x.
And, Elena says that 9x - 2x + 4x is equivalent to 11x, because the subtraction only applies to 2x.
Now,
Since, We know that;
⇒ 9x - 2x + 4x
⇒ 7x + 4x
⇒ 11x
Thus, Elena is correct as;
⇒ Elena says that 9x - 2x + 4x is equivalent to 11x, because the subtraction only applies to 2x.
Learn more about the subtraction visit:
https://brainly.com/question/17301989
#SPJ5
Use a model to divide. 1 ÷ 1/5
Answers
Answer: 5
Step-by-step explanation: just incase no one could see it
What is the excluded value?
0
1/2
1
Answers
Answer:
excluded value is 1/2
Step-by-step explanation:
The excluded value is the value when the denominator is equal to zero
1 -2x =0
Subtract 1 from each side
-2x = -1
Divide by -2
-2x/-2 = -1/-2
x = 1/2
The excluded value is 1/2