A certain quadratic function has x-intercepts at 2 and 3. What are the x-coordinates of its vertex?
a)7/2
b)1/2
c)3/2
d)5/2
Answers
Answer:
D
Step-by-step explanation:
The equation is going to by
y = (x - 2)(x - 3) Multiply to remove the brackets.
y = x^2 - 2x - 3x + 6
y = x^2 - 5x + 6 Now what you are going to do is complete the square.
y = (x^2 - 5x + __ ) +6
Take - 5
Divide it by 2 = -5 / 2
and square it = (-5 / 2)^2 = 25/4
Put this result inside the brackets.
y = (x^2 - 5x + 25/4 ) + 6 Now subtract 25/4 after the 6
y = (x^2 - 5x + 25/4) + 6 - 25/4
y = (x - 5/2)^2 - 1/4
The x coordinate of the vertex is 5/2
You could also do this by using x = -b/2a = - -5/2*1 = 5/2
Related Questions
PLZZZZ ANSWERrrrrrrrrrrr
Answers
Find the sum of: 72 − 104 + 5 and -32 + 4 - 10. What should be added to 32 + 32 + 3 to get 3 + 3 ? (1 mark) 3. Subtract the sum of 12ab –10bc –18ac and 9ab + 12bc + 14ac from the sum of ab + 2bc and 3bc – ac. Answer these with Explanation To be marked as BRAINLIEST!
Answers
Answer:
a). -65
b). -61
c). -20ab + 3bc +3ac
Step-by-step explanation:
According To the Question,
a). the sum of 72 − 104 + 5 and -32 + 4 - 10 .
(72 − 104 + 5) + (-32 + 4 - 10)(-27) + (-38)-27 - 38 -65b). What should be added to 32 + 32 + 3 to get 3 + 3 , Let X be Added .
Thus, (32 + 32 + 3) + X = 3 + 367 + X = 6X = 6 - 67X = -61c). Subtract the sum of 12ab –10bc –18ac and 9ab + 12bc + 14ac from the sum of ab + 2bc and 3bc – ac.
Thus, [(ab + 2bc) + (3bc – ac)] - [( 12ab –10bc –18ac) + (9ab + 12bc + 14ac)] (ab + 5bc - ac) - (21ab + 2bc - 4ac)ab + 5bc - ac - 21ab - 2bc + 4ac-20ab + 3bc + 3acYou are a botanist studying a rare flower. The center of the flower is a regular polygon. The petals coming off the flower are roughly triangular in shape.
a. What is the name of the center polygon?
b. What is the sum of the interior angles of the center?
c. What is the measure of each interior angle of the center?
d. In order to compare the size of the petals to other flowers of the same species you need to determine the exterior angle of the polygon. What is the measure of the exterior angle of the polygon?
Answers
Answer:
a). Regular Pentagon
b). 540°
c). 108°
d). 72°
Step-by-step explanation:
According To the Question
Given, a botanist studying a rare flower. The center of the flower is a regular polygon. The petals coming off the flower are roughly triangular in shape.a). the name of the center polygon is Regular Pentagon
b). the sum of the interior angles of the Regular Pentagon is 540°
c). the measure of each interior angle of the Regular Pentagon is 108°
d). the measure of the Each exterior angle of the Regular pentagon is 72° & Sum of All Exterior Angle Of Regular Pentagon is 360°
Use the function below to find F(3).
F(x) = 4•C**
O A.
H im
O B.
O c.
4
27
O D.
81
Answers
Answer:
4-3
Step-by-step explanation:
solve for x
Value of function f(x) = 4(1/3)ˣ when x = 3, f(3) = 4/27
Correct option is C.
What is exponential function?As the name suggests, the exponential function contains an exponent. Note, however, that the exponential function has a constant as its base and a variable as its exponent, not vice versa (if a function has a variable as its base and a constant as its exponent, it is a power function). The exponential function can be in one of the following forms:
Definition of exponential function
In mathematics, an exponential function is a function of the form f(x) = aˣ. where "x" is a variable and "a" is a constant called the base of the function, which must be greater than 0.
Given, exponential function
f(x) = 4(1/3)ˣ
exponential function is defined for x∈R
Putting x = 3
f(3) = 4(1/3)³
f(3) = 4/27
Hence, 4/27 is value of function f(x) = 4(1/3)ˣ when x = 3
Learn more about exponential function here:
https://brainly.com/question/14355665
#SPJ7
Which expression is equivalent to the given expression?
Answers
Answer:
Step-by-step explanation:
20cd^-1
An equation is shown below: −2(4x − 1) − 7 = 5 Which statement shows a correct next step in solving the equation? (1 point)
A)The equation can become −2(4x − 1) = −2 by applying the distributive property.
B)The equation can become −2(4x − 1) = 12 by applying the addition property of equality.
C)The equation can become −2(4x − 1) = 12 by applying the commutative property of addition
D)The equation can become −2(4x − 1) = −2 by applying the subtraction property of equality.
Answers
Answer:
B
Step-by-step explanation:
Add both sides of the equation by 7, which satisfies the definition of the addition property of equality.
Which of the following graphs is the solution set of -10 < 3x - 4 < 8?
Answers
Answer:
3rd option
Step-by-step explanation:
Solving the inequality
- 10 < 3x - 4 < 8 ( add 4 to each interval )
- 6 < 3x < 12 ( divide each interval by 3 )
- 2 < x < 4
Since -2 less than x and x less than 4
This is indicated by an open circle at - 2 and 4 on the number line and the line between them is shown in black.
The solution is represented on the 3rd graph
Answer:
its the 3rd graph
Step-by-step explanation:
pls help due today !!!!!!
Answers
Step-by-step explanation:
I don't know whether this is correct or not
Answer:
x = 2[tex]\sqrt{35}[/tex]
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
x² + b² = a² , that is
x² + 2² = 12²
x² + 4 = 144 ( subtract 4 from both sides )
x² = 140 ( take the square root of both sides )
x = [tex]\sqrt{140}[/tex] = [tex]\sqrt{4(35)}[/tex] = 2[tex]\sqrt{35}[/tex]
Which is the best description for the graph below?
A graph decreases from (0, 3) to (9, 0).
Answers
Answer:
Step-by-step explanation:
As we move from (0, 3) to (9, 0), we see x increasing by 9. This is the 'run.'
At the same time, we see y decreasing by 3. This is the 'rise.'
The slope of this line (graph) is m = rise / run = -3/9, or m = -1/3
Since we witness a decrease in y as we move from the first point to the second, we immediately suspect that the slope is negative.
All of the following numbers are rational except _____.
Answers
Answer:
What are the numbers?
Step-by-step explanation:
I can help if you give the numbers :)
i need help please. and explanation will help for tomorrow in a test:)
Answers
When you’re multiplying variables like the one in the problem above, instead of actually multiplying, you add. You only multiply in cases where there are coefficients.
Example : z^4 * z^2
Instead of multiplying, you would add the exponents together like so, z^6.
Which equation does the graph of the systems of equations solve?
two linear functions intersecting at 3, negative 2
Answers
Answer:
[tex]\text{B. }\frac{1}{3}x-3=-x+1[/tex]
Step-by-step explanation:
Let's start by taking a look at the blue line. The slope of any line that passes through two points is equal to the change in y-values over the change in x-values. We can see that the line passes through points (0, 1) and (1, 0). Assign these points to [tex](x_1,y_1)[/tex] and [tex](x_2, y_2)[/tex] (doesn't matter which you assign) and use the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let:
[tex](x_1,y_1)\implies (0,1)\\(x_2,y_2)\implies (1, 0)[/tex]
The slope is equal to:
[tex]m=\frac{0-1}{1-0}=\frac{-1}{1}=-1[/tex]
Therefore, the slope of this line is -1. In slope-intercept form [tex]y=mx+b[/tex], [tex]m[/tex] represents slope, so one of the lines must have a term with [tex]-x[/tex] in it, which eliminates answer choices A and D.
For the second line, do the same thing. The red line clearly passes through (0, -3) and (3, -2). Therefore, let:
[tex](x_1,y_1)\implies (0,-3)\\(x_2,y_2)\implies (3, -2)[/tex]
Using the slope formula:
[tex]m=\frac{-2-(-3)}{3-0}=\frac{1}{3}[/tex]
Thus, the slope of the line is 1/3 and the other line must have a term with [tex]\frac{1}{3}x[/tex] in it, eliminating answer choice C and leaving the answer [tex]\boxed{\text{B. }\frac{1}{3}x-3=-x+1}[/tex]
*You can find the exact equation of each line by using the slope formula as shown and plugging in any point the line passes through into [tex]y=mx+b[/tex]
factorise the following expressions;
1. 8x + 6 2. 4x + 2
Answers
Answer:
Step-by-step explanation:
1. 8x + 6
2(4x+3)
2.4x+2
2(2x +1)
Answer:
[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]
1. [tex]\boxed{Factorise \ = \ 8x + 6}[/tex]
⎆To factorise this, you have to take the common factor out. In this case, it's 2.
[tex]8x + 6 \\ = 2(4x + 3)[/tex]
[tex]\boxed{Answer \ = \ 2(4x + 3)}[/tex]
2) [tex]\boxed{Factorise \ = \ 4x + 2}[/tex]
⎆To factorise this, you have to take the common factor out. In this case also, it's 2.
[tex]4x + 2 \\ = 2(2x + 1)[/tex]
[tex]\boxed{Answer \ = \ 2(2x + 1)}[/tex]
____________________
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
ღ [tex]RainbowSalt2^{2}2^{2} [/tex]
The temperature in Anchorage, Alaska one morning was -8 degrees Fahrenheit. It rose slightly, increasing only 10 degrees by lunchtime. By dinnertime, the temperature had fallen 8 degrees. What was the ending temperature?
Answers
Answer:
The ending temperature was -6 degrees Fahrenheit.
Step-by-step explanation:
First, it was -8 degrees
Then, it was -8+10=2 degrees
Lastly, it was 2-8=-6 degrees
50 POINTS
Find the approximate values of the five-number summary for the data set represented by this box plot.
Answers
Answer:
From the box plot we get:
Minimum - 14Maximum - 88Quartile 1 - 34Quartile 3 - 65Median - 48Answer:
the other person is correct!
Step-by-step explanation:
Show them some love <3!
Please help ASAP!!
I'll mark brainliest!
Answers
Answer:
729 x [tex]\frac{1}{3}[/tex]^x
Step-by-step explanation:
the third option
- trial and error
The Jaxson Company offers a 6% coupon bond with semi-annual payments and a yield to maturity of 7.27%. The bonds mature in 6 years. What is the market price of a $1,000 face value bond?
Answers
Find the value of x and y. Write your answers in simplest form
Answers
=
7
√
3
,
y
=
14 hopefully it’s correct stream Nicki
Answer:
x = 16, y = 8[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using the sine ratio in the right triangle and the exact value
sin30° = [tex]\frac{1}{2}[/tex] , then
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{8}{x}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
x = 16
----------------------------------------------------------
Using Pythagoras' identity in the right triangle
y² + 8² = 16²
y² + 64 = 256 ( subtract 64 from both sides )
y² = 192 ( take the square root of both sides )
y = [tex]\sqrt{192}[/tex] = [tex]\sqrt{64(3)}[/tex] = 8[tex]\sqrt{3}[/tex]
Write
in function notation: h=x-2
Answers
Answer:
h(x) = x - 2
Step-by-step explanation:
h(x) = x - 2
Answer:
h(x) = x - 2
Step-by-step explanation:
help please!!..........
Answers
Answer: 0.36
Hope this helps...
Have a great day.
Which is the ratio formed when finding Tan M?
45
24
K
M M
51
15
17
1
15
8
8
15
8
17
Answers
Answer:
tanM = [tex]\frac{15}{8}[/tex]
Step-by-step explanation:
tanM = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{KL}{LM}[/tex] = [tex]\frac{45}{24}[/tex] = [tex]\frac{15}{8}[/tex]
PLEASE HELP HIRRYYYY PLEASEEE
Answers
Answer:
i believe the answer is B
Step-by-step explanation:
hope this helps
11. What is the perimeter of the garden?
Answers
Answer:
19[tex]\frac{1}{4}[/tex] or 18[tex]\frac{5}{4}[/tex]
Step-by-step explanation:
First, add the whole numbers
3, 7, and 8
18
Add the fractions
[tex]\frac{1}{2}[/tex]+[tex]\frac{3}{4}[/tex]=[tex]\frac{5}{4}[/tex]
IF YOU WANT SIMPLIFIED NUMBER DO THIS
[tex]\frac{5}{4}[/tex]=1[tex]\frac{1}{4}[/tex]
18+1[tex]\frac{1}{4}[/tex]=19[tex]\frac{1}{4}[/tex]
6. Find the area of the figure below. Round to the hundredths place.
Answers
Answer:
300.94 sq.m
Step-by-step explanation:
A solid in the shape of cylinder with two hemisphere to each of its ends.
Length of the entire solid = 18 mDiameter of the solid = 7 mRadius of hemisphere , r = 7 / 2 = 3.5 mTo findTotal surface area Formula UsedCurved surface area of hemisphere= 2π ×r ²Curved surface area of cylinder = 2 π × r × hSolution :-Finding, the Curved surface area of cylinder
Calculate the height of cylinder
Height of cylinder = total length of solid - 2 × radius of hemisphereHeight of the cylinder = 18 m - 2 × 3.5= 18 m - 7 mHeight of cylinder = 11 m
Now, we have
Height of cylinder = 11 m
Radius of cylinder = 7 / 2 = 3.5 m
Using Formula :-
Curved surface area of cylinder = 2× π × r × h
Substitute the values
Curved surface area of cylinder = 2π× 3.5m×11m.
Using the value of π = 3.14
Curved surface area of cylinder =2×3.14× 3.5m × 11 m.
multiply, we get.
Curved surface area of cylinder = 241.78 m².
Finding curved surface area of hemisphere
Using Formula
Curved surface area of hemisphere = 2 × π × r²
substitute the values into the formula
Curved surface area of hemisphere = 2 π × ( 3.5 )²
Evaluate the exponent
Curved surface area of hemisphere =2π×12.25m².
Using value of π = 3.14
Curved surface area of hemisphere = 2 × 3 14 × 12.25 m ²
multiply , we get
Curved surface area of hemisphere = 76.93 m².
Find the total areaTotal area of capsules = Curved surface area of cylinder + 2 (Curved surface area of hemisphere)
Total surface area of capsules = 241.78 m²+ 2 × 76.93 m².
Total surface area = 241.78m² + 153.86m².
Subtract and finally we get
Total surface area = 395.64 m ²
Complete the table. Function: f (x) = x+2
Answers
4:(6)
7:(8)
8:(9)
A gnat's eye is 0.012
inches wide. A fly's eye is
2.4 x 10-1 inches wide.
How much larger is the
fly's eye?
Answers
point e is the midpoint of ca and bd. which statements about the diagram are true?
Answers
Answer:
Step-by-step explanation: i don’t know to be honest
Evaluate -8•|2|
-10
10
-16
16
Answers
Answer:
-16
Step-by-step explanation:
-8•|2|
Absolute value means take the positive value of the number inside
-8 * +2
Multiply
-16
Mrs. Easton plans to hire a balloon artist for her daughter's birthday. The graph shows the cost per hour to hire the artist.
If there are more than 10 children at the party, the balloon artist charges an additional supply fee of $35. There will be 15 children at the Easton party. How much will the balloon artist charge Mrs. Easton for a party that is 4.5 hours long?
Multiple choice question.
A)
$60.25
B)
$67.50
C)
$98.75
D)
$102.50
Help ASAP
Answers
Explanation:
Answer:
I believe it is A) 60.25
Step-by-step explanation:
If it is not correct, let me know.
Help me please no links no
Answers
Answer:
x/4
Step-by-step explanation:
x + 4/4 = y + 3/3
do cross multiplication
4(y +3)=3(x +4)
4y +12=3x +12
4y=3x + 12 -12
4y=3x
y/3 = x/4
