The sum of three of the interior angles of a pentagon is 420°. If the remaining angles are equal, how much does each measure?
Write the quadratic function in the form f (x) = a (x - h)2 + k.
Then, give the vertex of its graph.
f (x) = – 2x² + 16x – 30
Writing in the form specified: f(x)=???
Vertex: (?,?)
Answer:
The vertex form is:
[tex]f(x)=-2(x-4)^2+2[/tex]
Where the vertex of the function is (4, 2).
Step-by-step explanation:
We want to find the vertex and the vertex form of the quadratic function:
[tex]f(x)=-2x^2+16x-30[/tex]
We have two methods of converting from standard form to vertex form: (1) by using the vertex formulas or (2) by completing the square.
Method 1) Using Formulas:
First, note that the leading coefficient of our function is -2.
The vertex of a quadratic equation is given by the formulas:
[tex]\displaystyle \text{Vertex}=\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]
In this case, a = -2, b = 16, and c = -30. Find the x-coordinate of the vertex:
[tex]\displaystyle x=-\frac{(16)}{2(-2)}=\frac{-16}{-4}=4[/tex]
In order to find the y-coordinate of the vertex, we substitute this value back in. Hence:
[tex]f(4)=-2(4)^2+16(4)-30=2[/tex]
Therefore, our vertex is (4, 2).
Vertex form is:
[tex]\displaystyle f(x)=a(x-h)^2+k[/tex]
Where a is the leading coefficient and (h, k) is the vertex.
Substitute. Our leading coefficient is -2 and our vertex is (4, 2). Therefore:
[tex]\displaystyle f(x)=-2(x-4)^2+2[/tex]
Method 2) Completing the Square:
To complete the square, we first factor out the leading coefficient from the first two terms:
[tex]f(x)=-2(x^2-8x)-30[/tex]
Then, we divide the coefficient of the b term by half and square it. This yields:
[tex]\displaystyle \left(\frac{-8}{2}\right)^2=16[/tex]
We will add this value inside of the parentheses. Since we added 16 inside the parentheses, we will subtract 16 outside of the parenthese to remain the equality of the function. However, since the parentheses is multiplied by -2, we technically added -2(16) = -32 inside. So, we will subtract -32 outside. Thus:
[tex]f(x)=-2(x^2-8x+16)-30-(-32)[/tex]
Simplify:
[tex]f(x)=-2(x^2-8x+16)+2[/tex]
Factor using the perfect square trinomial:
[tex]f(x)=-2(x-4)^2+2[/tex]
We acquire the same result.
Choose the answer that makes the sentence true.
Answer:
I would answer but I don't know what the answers are...
Answer:
I cant see the answers, any way you can get it up?
The Duke Blue Devils basketball team plays home games at Cameron Indoor Stadium. The court is in the shape of a rectangle. If the length of the court is (5.8a+6.1b-3.6c) feet and the width of the court is (434b-235c) feet, then what is the perimeter of the court?
Answer:
11.6a + 880.2b - 477.2c
Step-by-step explanation:
Given:
length of the court = (5.8a+6.1b-3.6c) feet
width of the court = (434b-235c) feet
Since the court is said to be rectangular in shape :
The perimeter of a rectangle = 2(length + width)
Perimeter = 2(5.8a+6.1b-3.6c + 434b-235c)
Perimeter = 2(5.8a+6.1b+434b-3.6c-235c)
Perimeter = 2(5.8a + 440.1b - 238.6c)
Perimeter = 11.6a + 880.2b - 477.2c
I need help can someone please answer this for me
Question 4 OT TU
Find the volume of the cube in inches and enter your answer below. Round
your answer to the nearest hundredth. Do not include units in your answer.
3.2 in.
3.2 in.
3.2 in.
Answer here
Answer:
The volume of cube is 32.7 inches³
Step-by-step explanation:
Given :-
Side of cube is 3.2 inTo Find :-
Volume of cube
Formula Used :-
Volume of cube = ( side)³
Solution :-
To calculate the volume of cube. Simply by applying formula volume of cube. As given in the question that ths side if cube is 3.2 inches.Using Formula
Volume of cube = ( side) ³
Where,
side of cube is 3.2 inchesCalculation being :-
⟼ Volume of cube = ( 3.2 inches) ³
⟼ Volume of cube = 32.768 inches ³
Hence, the volume of cube is 32.768 inches³.
Round nearest hundred = 32.7 inches³.
What is the equation of the parabola with focus (1/3, 2/3) and directrix y = 1/2pls help ill give points
Answer:
D. y = 3·x² - 2·x + 11/12
Step-by-step explanation:
The coordinates of the focus of the parabola, f = (1/3, 2/3)
The directrix of the parabola, y = 1/2
The standard form of the equation of a parabola is (x - h)² = 4·p·(y - k)
The coordinates focus = (h, k + p)
The y-coordinates of the directrix, y = k - p
By comparison, we have;
h = 1/3...(1)
k + p = 2/3...(2)
k - p = 1/2...(3)
Adding equation (3) to equation (2) gives;
k + p + (k - p) = k + k + p - p = 2·k = 2/3 + 1/2 = 7/6
k = (7/6)/2 = 7/12
k = 7/12
From equation (2), we get;
p = 2/3 - k
∴ p = 2/3 - 7/12 = 1/12
p = 1/12
The equation of the parabola is therefore;
(x - 1/3)² = 4·(1/12)·(y - 7/12) = y/3 - 7/36
y = 3 × ((x - 1/3)² + 7/36) = 3 × ((x² - 2·x/3 + 1/9) + 7/36) = 3·x² - 2·x + 11/12
y = 3·x² - 2·x + 11/12.
Two similar triangles have a scale factor of 5:3. The perimeter of the larger triangle is 75 sq inches. What is the perimeter of the smaller triangle measured in inches?
Answer:
45 inches
Step-by-step explanation:
Create a proportion where x is the perimeter of the smaller triangle:
[tex]\frac{5}{3}[/tex] = [tex]\frac{75}{x}[/tex]
Cross multiply and solve for x:
5x = 225
x = 45
So, the perimeter of the smaller triangle is 45 inches
Oliver earns an hourly wage, as shown in the graph. In addition to his hourly wage, he is eligible for bonuses. If he received a $100 bonus award for his performance and worked 20 hours, how much did he earn?
Oliver earns a total of $260.
What is Ratio?When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b. An equation in which two ratios are made equal is known as a percentage.
Given, In the graph, Oliver is depicted as having hourly pay. He is qualified for bonuses in addition to his hourly pay. If he put in 20 hours of effort and received a $100 performance bonus. equation of this line:
y = kx +c
since this line goes through the origin point. Constant (c) will be zero.
At the point (1, 8 ) k = 8
Hence, Y = 8x
Because hours worked are 20
earning = 8 * 20 = 160
Total earnings = 100 + 160 = 260
Therefore, the Total money that Oliver earns is $260.
Learn more about ratios here:
https://brainly.com/question/29192438
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someone PLSSSS HELPPP !! fast pls please
Answer:
A. i think
Step-by-step explanation:
Answer:
4, -16, 64, -256
the common ratio is -4
Step-by-step explanation:
Can you please help me. It says to find each product
Here is the question
There is a picture
Answer:
-3/5
Step-by-step explanation:
7 * -3/7 * 1/5
Rewritng
7/7 * -3/5 *1
Simplifying fractions
1 * -3/5 *1
-3/5
Help me to do this question
Answer:
140°
Step-by-step explanation:
a° = 180°-(75°-35°) = 180°-40° = 140°
The endpoints of a diameter of a circle are (2, 4) and (-4, 7).
What is the standard form of the equation of this circle?
Enter your answer by filling in the boxes. Enter any fractions in simplified form.
X
Answer:
(x+1)²+(y-5.5)²=45/4.
Step-by-step explanation:
1) the common form of the required equation is: (x-a)²+(y-b)²=r², where 'a' and 'b' are the coordinates of the centre of the given circle, r - radius of the given circle.
2) the midpoint of the diameter is the centre of the given circle, its coordinates are:
[tex]\frac{2-4}{2}=-1; \ and \ \frac{4+7}{2}=5.5.[/tex]
3) the length of the radius of the given circle is:
[tex]r=\frac{1}{2}*\sqrt{(2+4)^2+(4-7)^2)}=\sqrt{\frac{45}{4}}.[/tex]
4) according to the common form and calculated the centre O(-1;5.5) and the radius it is possible to make up the required equation of the circle:
[tex](x+1)^2+(y-5.5)^2=\frac{45}{4}.[/tex]
Answer:
The correct answer is (x+1)^2 + (y−11/2)^2 = 45/4
Step-by-step explanation:
This is how the system wants it put in. See question 12
PLSSS, NEED ANSWER. Find the midpoint of the line segment with end coordinates of (-2,-5 and 3,-2
). Give coordinates as decimals where apropriate
Answer:
(0.5, -3.5)
Step-by-step explanation:
(x1 + x2/2, y1 + y2/2)
(-2 + 3 / 2, -5 - 2 / 2)
(1/2, -7/2)
he table represents the multiplication of two binomials.
A geometric model with 2 columns and 2 rows. The first column is labeled 3 x with entries A, C. The second column is labeled 5 with entries B, 10. The first row is labeled negative x with entries A, B. The second row is labeled 2 with entries C, 10.
What is the value of A?
negative 3 x
negative 3 x squared
negative 5 x
negative 5 x squared
Answer:
B.
Step-by-step explanation:
If you add 3x + x, it would be 3x^2
Multiple Choice:
Suppose a triangle has sides 3, 4, and 5. Which of the following MUST be true?
A. The triangle in question may or may not be a right triangle.
B. The triangle in question is a right triangle.
C. The triangle in question is not a right triangle.
Answer:
b. the triangle is not a right triangle
Step-by-step explanation:
Answer:
The triangle in this particular question may or may not be a right angled triangle
Step-by-step explanation:
~basically triangle are known to have 3 sides otherwise we would not call it a triangle...however in this particular question they may be no definite answer and triangle with 3 sides can be any sort of triangle:
-isosceles triangle with 3 uneven sides
-right angled triangle like stated with an hypotenuse
or
-scalene triangle with simply to equal sides...
glad I could help thumbs
disclaimer this answer may not be accurate and I do not take any responsibility if this answer is wrong thank you
give that y=-4,x=3,b=7 & c=2 find b^c
Answer:
49
Step-by-step explanation:
b^c
Let b = 7 and c = 2
7^2
7*7 = 49
Answer:
49
Step-by-step explanation:
you fill in the equation so that it's 7^2. which is 7*7. this equals 49
the window of a building 65m above the street level from this window ,a person looks across the street at a building and finds that the Angle of elevation of the top of the building is 72°and the angle of depression if the bottom of the building is 28° .if the street level is horizontal and the ground distance between the building is 80m.find to the nearest m the vertical heights of the building
not so sure about your question. please check.
Área de Cuadriláteros
¿Me pueden ayudar con esta tarea?
Answer:
I can't understand this language sorry
Work out(3^5-5^3+2) divided 4^2
Given:
[tex](3^5-5^3+2)[/tex] divided by [tex]4^2[/tex].
To find:
The simplified form of the given expression.
Solution:
We have, [tex](3^5-5^3+2)[/tex] divided by [tex]4^2[/tex]. Mathematically it can be written as:
[tex]\dfrac{3^5-5^3+2}{4^2}=\dfrac{243-125+2}{16}[/tex]
[tex]\dfrac{3^5-5^3+2}{4^2}=\dfrac{120}{16}[/tex]
[tex]\dfrac{3^5-5^3+2}{4^2}=\dfrac{15}{2}[/tex]
[tex]\dfrac{3^5-5^3+2}{4^2}=7.5[/tex]
Therefore, the simplified form of the given expression is 7.5.
P is directly proportional to (q + p)^2. Q is 1 when p is 1. Find the equation connectng q to p and find q when p is 10
Answer:
A directly proportionality between x and y is written as:
y = k*x
where k is the constant of proportionality.
Then, if p is directly proportional to (q + p)^2
We can write this as:
p = k*(q + p)^2
Now we know that q = 1 when p = 1
Then we can replace these values in the above equation to find the value of k
1 = k*(1 + 1)^2
1 = k*2^2 = k*4
1/4 = k
Then the equation is:
p = (1/4)(p + q)^2
Now we want to find the value of q when p = 10
So we just replace p by 10, and solve the equation
10 = (1/4)*(q + 10)^2
10*4 = (q + 10)^2
40 = q^2 + 2*q*10 + 10^2
40 = q^2 + 20*q + 100
This is a quadratic equation for q, such that:
q^2 + 20*q + 100 - 40 = 0
q^2 +20*q + 60 = 0
This is the equation that gives the value of q when p = 10
To solve this, we can use Bhaskara's equation, which says that for a quadratic equation:
a*x^2 + b*x + c = 0
The solutions are given by:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4*a*c} }{2*a}[/tex]
In this case, the solutions for q are:
[tex]q = \frac{-20 \pm \sqrt{20^2 - 4*1*60} }{2*1} = \frac{-20 \pm 12.65}{2}[/tex]
Then we have two possible values for q:
q = (-20 + 12.65)/2 = -3.675
q = (-20 - 12.65)/2 = -16.325
Anthony is building a cube-shaped box to store some of his smaller crafting supplies. The formula for the surface area of a cube is SA = 6s 2 , where s is the side length of the cube. If he has a total of 200 in. 2of cardboard, can Anthony build a box where s = 6 in.?
A) No, he needs 16 in. 2more cardboard.
B) No, he needs 232 in. 2more cardboard.
C) Yes, he will have 56 in. 2of cardboard left over.
D) Yes, he will have 128 in. 2of cardboard left over
Answer:
I'll go through the setup and let you compute the answer
Step-by-step explanation:
I think you meant
[tex]SA = 6 {s}^{2} [/tex]
and the sheet of cardboard if
[tex]200 {in}^{2} [/tex]
Find the surface area of a 6 inch cube
[tex]SA = 6 \times {6}^{2} [/tex]
if you have questions, you can send a comment
Please hurry i want the answer of this question please
[tex]\displaystyle\bf 1200=12*100=3*4*(2*5)^2=3*2^2*2^2*5^2=2^4*3^1*5^2 \\\\Answer: \boxed{ A)\quad a=4 \quad ; \quad b=1 \quad ; \quad c=2}[/tex]
Which word BEST describes 3x, 5y, and z in the expression 3x − 5y + z?
A terms
B products
C variables
D coefficients
PLEASE HELP HURRY ASAP
The spinner depicted is a fair spinner. The spinner is least likely to land on which number?
A. 1
B. 2
C. 3
D. it is impossible to tell
Find the inverse of the function y = 2x^2 + 2.
Answer:
its the last one.
Step-by-step explanation:
easy way to do inverse functions:
write out equation :
y = 2[tex]x^{2}[/tex] + 2
Switch the x and y:
x = 2[tex]y^{2}[/tex] + 2
Solve for y :
x = 2[tex]y^{2}[/tex] + 2
subtract 2 both sides
x - 2 = 2[tex]y^{2}[/tex]
Divide both sides by 2
[tex]\frac{x}{2}[/tex] - [tex]\frac{2}{2}[/tex] = [tex]y^{2}[/tex]
reduce fraction and square root both sides
Plz hep me I don’t understand
Answer:
Purple
Step-by-step explanation:
Because the graph has the circle filled in at the point 11, we know that it is a valid solution and that we are looking for a sign with the line under it. However, because we know that the number line extends to the right of 11, these would include answers such as 12, 13, 14, 15, etc. Because all these values are "greater than or equal to" 11, our answer is 11 <or= a, which is the purple one or the one on the right.
0. 00147 in standard form
Answer:
Answer: It can be written as 1.47x10-³
Step-by-step explanation:
0.00147 = 1.47
1.47 = 1.47 x 10 -^3
what is the quotient
4/5 ÷ 1/10
Answer:
4/5 ÷ 1/10 = 40/5 as simplified as 8/1 in fraction form.
4/5 ÷ 1/10 = 8 in decimal form.
This calculator, formula, step by step calculation and associated information for fraction 4/5 divided by 1/10 may help students, teachers, parents or professionals to learn, teach, practice or verify such division between two fractions calculations efficiently.
Step-by-step explanation:
hope it helps...
Answer:
8/1
Step-by-step explanation:
4/5 change × 10/1= 8/1 hope helpful answer to your question have a good time to you
mobimax Which of the following statements are true of rational numbers?
Check all that are true.
Decimals that can be written as fractions are rational numbers.
Repeating decimals are rational numbers because they can be written as fractions.
One divided by zero is an example of a rational number.
A rational number can be written as one integer divided by another integer.
Rational numbers can be written as fractions.
Answer:
Options : 1 , 2 , 4 , 5
Step-by-step explanation:
Rational numbers are numbers of the form
[tex]\frac{p}{q}[/tex],
where p and q are integers and q≠0
A decimal number is a rational number , if its :
A) Terminating.
Example : 0.5
B) Non Terminating and Recurring(repeating).
Example : 0.111111111.....
Option 1 : True
Option 2 : True
Option 3 : False [ denominator cannot be zero ]
Option 4 : True
Option 5 : True