Answer:
Part A) The graph in the attached figure
Part B) see the explanation
Step-by-step explanation:
Part A) Graph the function
we have the quadratic function
[tex]y=3x^2-12x-36[/tex]
This is a vertical parabola open upward
The vertex is a minimum
using a graphing tool
The graph in the attached figure
Part B) What are the values of a, b and c?
we know that
The values of a and b represent the x-intercepts of the quadratic equation
The x-intercepts are
(-2,0) and (6,0)
so
[tex]a=-2\\b=6[/tex]
Find the value of c
we know that
The x-coordinate of the vertex in a vertical parabola is equal to the midpoint of the roots
so
The value of c is equal to
[tex]c=\frac{a+b}{2}[/tex]
substitute the given values
[tex]c=\frac{-2+6}{2}=2[/tex]
see the attached figure
Question 1
Determine the midpoint of the segment with endpoint (-9,3) and (7,-8).
Question 2
Answer:
(-1, -2.5)
Step-by-step explanation:
the midpoint of a segment is [tex](\frac{x1+x2}{2} ,\frac{y1+y2}{2}[/tex][tex])[/tex], given points (x1, y1) and (x2, y2)
[tex]midpoint=(\frac{-9+7}{2}, \frac{3-8}{2} )[/tex] [tex]= (\frac{-2}{2}, \frac{-5}{2} ) = (-1, -2.5)[/tex]
Answer:
m (-1, -2.5)
Step-by-step explanation:
x1=-9 x2=7 y1= 3 y2=-8
-9+ 7 3+ -8
m= ------------ , -----------
2 2
m= -2/2, -5/2
m (-1, -2.5)
Prove algebraically what type of function this is (even, odd, or neither).
The given function is even.
Solution:
Given function:
[tex]f(x)=x^{6}-x^{4}[/tex]
If f(-x) = -f(x), then the function is odd.
If f(-x) = f(x), then the function is even.
[tex]f(x)=x^{6}-x^{4}[/tex]
Substitute x = -x
[tex]f(-x)=(-x)^{6}-(-x)^{4}[/tex]
[tex]=x^{6}-x^{4}[/tex]
= f(x) (given)
f(-x) = f(x)
From the definition, it is even.
Hence the given function is even.
Determine the center and radius of the following circle equation:
x2 + y2 – 12x – 18y + 108 = 0
Center:
Radius:
Pls help :)
Answer:
(6, 9 ) and r = 3
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given
x² + y² - 12x - 18y + 108 = 0
Rearrange the x- terms and the y- terms together and subtract 108 from both sides, that is
x² - 12x + y² - 18y = - 108
To obtain standard form use the method of completing the square
add ( half the coefficient of the x and y terms )² to both sides
x² + 2(- 6)x + 36 + y² + 2(- 9)y + 81 = - 108 + 36 + 81
(x - 6)² + (y - 9)² = 9 ← in standard form
with centre = (6, 9 ) and r = [tex]\sqrt{9}[/tex] = 3
Regina is tying a bow around a soccer ball to give to her sister. The ball has a radius of 4.5 inches. If the ribbon needs to be 10 inches longer than the circumference of the ball so she has enough room to tie a bow , how many inches of ribbon will she need?
The circumference of the soccer ball can be found using the formula for the circumference of a circle, to which 10 inches is then added to find the total length of the ribbon Regina needs.
Explanation:The problem involves understanding the mathematical concept of circumference. The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. In this case, the soccer ball has a radius of 4.5 inches. Therefore, the circumference of the soccer ball would be C = 2π(4.5) inches.
Then, the problem states that the ribbon needs to be 10 inches longer than the circumference of the ball. So the total length of the ribbon that Regina needs is C + 10 inches. By substituting the values, we get the length of the ribbon needed.
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5(y+1)=30 solve for y
Answer:y=5
Step-by-step explanation:
5(y+1)=30
Divide both sides by 5
5(y+1)/5=30/5
We get y+1=6
Subtract 1 from both sides
y+1-1=6-1
We get y=5
What is the slope indicated
in the table below
X 0 1 2 3
Y 0 5 10 15
Answer:
5
Step-by-step explanation:
1. Identify the changes (Δ) in each consecutive pair of x-values and y-values
The changes in x (Δx) are 1, 1, and 1. The changes in y (Δy) are 5, 5, and 5.
2. Calculate the corresponding values of Δy/Δx
In each case, Δy/Δx = 5.
The slope is 5.
I have organized the calculations in the table below.
[tex]\begin{array}{cc|cc|c}\mathbf{x} & \mathbf{\Delta x} & \mathbf{y} & \mathbf{\Delta y} & \mathbf{\Delta y/ \Delta x} \\0 & & 0 & & \\ & 1 & & 5 & \mathbf{5} \\1 & & 5 & & \\ & 1 & & 5 & \mathbf{5} \\2 & & 10 & & \\ & 1 & & 5 & \mathbf{5} \\3 & & 15 & & \\\end{array}[/tex]
15 is 0.2% of what number? Please answer!
Answer:
7500
Step-by-step explanation:
0.2 x 7500 divided by 100 =15
Use substitution to find th
7) 4x – 2y = -22
-x+ y=3
Answer:
y = -5
Step-by-step explanation:
x= (-22+2y)/4 = -3+y
-22+2y = 4(-3+y)
-22+2y = -12+4y
-22+12 = 4y-2y
-10 = 2y
-10/2 = y
-5 = y
Answer:
x = -8
y = -5
Step-by-step explanation:
From the given expression, let's make two equations
4x - 2y = - 22--------------------------(i)
-x + y = 3-----------------------------(ii)
to easily substitute, lets make another equation from equation (ii)
y = 3 + x
substitute (y=3+x) in equation (i)
4x - 2 (x+3) = -22
4x - 2x - 6 = -22
2x - 6 = -22
2x = -22 + 6
2x = - 16
x = -16 / 2
x = - 8
lets solve for (y) by substituting (x = - 8) in equation (ii)
- (- 8) + y = 3
8 + y = 3
8 + y = 3
y = 3 - 8
y = - 5
Therefore:
x = - 8
y = - 5
PLEASE FIND ATTACHED FILE
Maths is fun, keep learning!
3. Select True or False for each statement about the function y = -9x - 4.
A. The coefficent of x2 is 1.
B. The graph of the function opens up.
000001
tooooo
C. The graph of the function is not a straight line.
D. For positive values of x, as x increases the function decreases,
E. The function does not contain the origin.
Answer: Teacher graded mine and it was: false, true, true, false, true
Step-by-step explanation:
What is the measure of ∠P, to the nearest degree?
24°
42°
55°
101°
A scalene triangle P Q R. Side P Q is labeled as 5 feet. Side Q R is labeled as 10 feet. Side P R is labeled as 12 feet.
Answer:
55°
Step-by-step explanation:
use The Law of Cosines
cos p = (PR² + PQ² - QR²) / 2 x PR x PQ
= (144 + 25 - 100) / 120
= 69 / 120
=0.575
∠P = 55°
Answer:
55 degrees
Step-by-step explanation:
i took the test
the difference between a number and 8 is more than 4
Answer:
x= 13, 14, 15
Step-by-step explanation:
x-8 > 4
+8 +8
x > 12
13
14
15
Decide if each sample is random. Explain why or why not.
a. Asking every 15th person on the school roster if they buy lunch in the cafeteria or bring lunch from
home.
b. Measuring the height of all the sunflowers to find the mean height of all the flowers in a garden.
Answer:
a- no they are polling
b-yes there is no point
Step-by-step explanation:
If both figures have the same perimeter what is the perimeter of each figure,
Yo sup??
perimeter of figure 1 is
2(x+x+5)=2(2x+5)
perimeter of figure 2 is
3x+22
now
4x+10=3x+22
x=12
Hope this helps
Answer:
The correct answer is 58.
Hope this helped!
PLZ HELP!!!!!!!! due in 30 minutes im timed!
Answer:
For x=20: difference is 22
Step-by-step explanation:
For f: y increased 5 units (from 1 to 6) when x went from 0 to 10. Being linear, when x=20, f will increase with another 5 units, being 6+5=11.
For g: g(20)=1.5×20+3=33
So, for x=20, f(20)-g(20)=11-33=-22
So the difference is 22.
Solve for x. Write the smaller solution first, and the larger solution second. (3x -6)(-x +3)=0(3x−6)(−x+3)=0
x= 2,3
hope that helped
translate “a number x divided by 5 is at least -19” into a inequality
Answer: x/5 ≥ -19
Step-by-step explanation:
10-ounce package of cashews costs $8.11, and a 16-ounce package of cashews costs $12.
a. What is the cost per ounce for the 10-ounce package of cashews?
b. What is the cost per ounce for the 16-ounce package of cashews?
c. Which package is the better buy?
a. $0.811
b. $0.75
c. 10-ounce package of cashews costs $8.11 is better then a 16-ounce package of cashews costs $12
Step-by-step explanation:
Here we have , 10-ounce package of cashews costs $8.11, and a 16-ounce package of cashews costs $12.
a. What is the cost per ounce for the 10-ounce package of cashews?
cost per ounce for the 10-ounce package of cashews = [tex]\frac{8.11}{10}[/tex]
cost per ounce for the 10-ounce package of cashews = $[tex]0.811[/tex]
b. What is the cost per ounce for the 16-ounce package of cashews?
cost per ounce for the 16-ounce package of cashews = [tex]\frac{12}{16}[/tex]
cost per ounce for the 16-ounce package of cashews = $[tex]0.75[/tex]
c. Which package is the better buy?
10-ounce package of cashews costs $8.11 is better then a 16-ounce package of cashews costs $12 , because cost per ounce for the 10-ounce package of cashews = $[tex]0.811[/tex] is greater then cost per ounce for the 16-ounce package of cashews = $[tex]0.75[/tex]
The cost per ounce for the 10-ounce package of cashews is $0.811, and the cost per ounce for the 16-ounce package is $0.75. The 16-ounce package is the better buy.
Explanation:a. To find the cost per ounce for the 10-ounce package of cashews, we divide the total cost by the number of ounces. $8.11 ÷ 10 ounces = $0.811 per ounce.
b. To find the cost per ounce for the 16-ounce package of cashews, we divide the total cost by the number of ounces. $12 ÷ 16 ounces = $0.75 per ounce.
c. The better buy is the package with the lower cost per ounce. Therefore, the 16-ounce package of cashews is the better buy.
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What is 2 times the difference of 73 and twice the sum of 9 and 4?
This results in a final answer of 94.
The question asks for the calculation of 2 times the difference of 73 and twice the sum of 9 and 4. Let's break it down step by step:
First, calculate the sum of 9 and 4, which is 9 + 4 = 13.Next, multiply this sum by 2 to get twice the sum, which results in 13 imes 2 = 26.The difference between 73 and the result from step 2 is 73 - 26 = 47.Finally, multiply that difference by 2 as per the question, giving us 47 imes 2 = 94.Therefore, 2 times the difference of 73 and twice the sum of 9 and 4 equals 94.
Explain why receiving a 15% discount is the same as finding 85% percent of the original cost of an item. Then, explain how the mathematical properties and equivalent expressions helped them understand and solve the problem. Please answer!!
Answer:
15% discount means you're paying 85% of the marked price because total is 100% and 100-15 = 85%
Let X be the naked price
Paid = marked price - discount
Paid = X - (15/100 × X)
Using distribution property,
Paid = X(1 - 15/100)
Paid = X[(100-15)/100]
Paid = X(85/100)
Which is 85/100 × X
Hence 85% of X
Answer: 85% = 0.85
While 15% = 0.15
Step-by-step explanation:
Percentage is a fraction whose denominator is 100. So if we say 15%, we mean 15/100 = 0.15.
If want to find 15% of a 100, it means 15% of 100 = 15/100 × 100 = 15.
To find 85 % of 100 means 85/100 × 100= 85
hence subtraction of 15% from 100% is 85%
Therefore 15% = 15/100 = 0.15
While 85% is 85/100 = 0.85
the perimeter of an equilateral triangle is givn as 15x+30. write two different expressions to represent the perimeter. use factoring to write one of the expressions
Answer:
15x+30 ; 15(x+2)
Step-by-step explanation:
You can write it as it is:
15x+30
OR
15(x+2)
5. Find the measure of angle A
Answer:
where is the angle if angle is not there nobody can answer this question.
Drag a statement or reason to each box to complete this proof. If −3(x+8)=−21, then x=−1.
Answer:
Yes, this is true.
Step-by-step explanation:
If you substitue x for -1 you get -3(-1+8)=-21, Then you add -1 and 8 so you should get 7. After, you multiply 7 times -3 you get -21. Proving this statement is correct.
Answer:
See below.
Step-by-step explanation:
We can solve for x:
−3(x+8) = −21
Distribute the -3 over the parentheses:
-3x - 24 = -21
Add 24 to both sides:
-3x -24 + 24 = -21 + 24
-3x = 3
Divide both sides by -3:
x = -1.
So that proves the original equation.
3/16 Problem Of The Day:
The following expression represents the school’s cost for 6 students to attend an after school event.
6(2k + 5) - 20
Part A: Simplify the expression using the Distributive Property.
Part B: If k = $12.50, what is the school’s cost for the event?
Answer:
A) 12k + 10
B) $160
Step-by-step explanation:
6(2k + 5) - 20
12k + 30 - 20
12k + 10
k = 12.5
12(12.5) + 10 = 160
Answer:
12k +10
Final cos = 160
Step-by-step explanation:
6(2k + 5) - 20
Distribute the 6
6*2k + 6*5 -20
12k +30 -20
12k +10
Let k =12.5
12*12.5 +10
150 +10
160
What are the coordinates for the vertices of the figure? *show your work*
The coordinates for the shape are;
a = (0, 0), b = (a, 0), c = (a, a), and d = (0, a).
Step-by-step explanation:
Step 1:
First, we must assign letters to the four vertices of the given shape.
Assume the lower-left vertex is a, the lower-right vertex is b, the upper-right vertex is c and the upper-left vertex is d.
So the vertices for the shape are a, b, c, and d.
Step 2:
The coordinates for a point on a graph is given by (x coordinate, y coordinate).
So we need to determine the x and y coordinates for the four points on the shape abcd.
Step 3;
The x coordinate for vertex a = 0, the y coordinate for vertex a = 0,
so the coordinates of vertex a = (0, 0).
The x coordinate for vertex b = a - 0 = a, the y coordinate for vertex b = 0,
so the coordinates of vertex b = (a, 0).
The x coordinate for vertex c = a- 0 =a, the y coordinate for vertex c = a- 0= a, so the coordinates of vertex c = (a, a).
The x coordinate for vertex d = 0, the y coordinate for vertex d = a - 0 =a,
so the coordinates of vertex d = (0, a).
Suppose 40 people come to your
party. If 15% of your guests arrive
early, how many people arrive early?
Step-by-step explanation:
15% as a decimal is 0.15
40*0.15 is 6
6 guests arrive early
6 people arrive early to the party.
Calculating the Number of People Who Arrive Early to a Party
To calculate the number of people who arrive early to a party where 40 people are expected, we use the given percentage of guests that arrive early, which in this case is 15%. The calculation process is straightforward:
Convert the percentage to a decimal by dividing by 100, which gives us 0.15.
Multiply the decimal by the total number of people expected at the party to find the number of people who arrive early.
So, the calculation is:
0.15 x 40 = 6
Therefore, 6 people arrive early to the party.
enter the ratio on its simplest form 9/12
Answer: 3/4
Step-by-step explanation:
To take this ratio to its simplest form, we have to divide by a value divisible by the numerator and denominator.
3 is a divisible value, therefore,
9/12 = 9 ÷ 3 = 3
12 ÷ 3 = 4
Thus, 9/12 = 3/4
I hope this helps.
where does the line y= -3x+7 cross the y-axis
Answer:
(0, 7 )
Step-by-step explanation:
Where the line crosses the y- axis the x- coordinate of the point is zero.
Substitute x = 0 into the equation and evaluate for y
y = - 3(0) + 7 = 0 + 7 = 7 ⇒ (0, 7 )
susie is painting a wall that is 12 feet tall and 9 feet wide if each can of paint has enough paint to cover 8 square feet how many cans of paint will susie need to cover the whole wall
Answer:13.5
Step-by-step explanation:
x= 12*9/ 8
13.5 paints are needed bro
i hope you understand the ans
i didnt add statments
By applying formula of area of rectangle we got that if susie is painting a wall that is 12 feet tall and 9 feet wide if each can of paint has enough paint to cover 8 square feet then total 12 cans of paint will susie need to cover the whole wall
What is rectangle ?Rectangle is a regular quadrilateral with all angle equal to right angle.
Given that wall that is 12 feet tall and 9 feet wide
So area of rectangle = length[tex]\times[/tex]width
Area= [tex]12\times 8=96[/tex]
Given that each can of paint has enough paint to cover 8 square feet
Hence number of cans required = 96/8=12
By applying formula of area of rectangle we got that if susie is painting a wall that is 12 feet tall and 9 feet wide if each can of paint has enough paint to cover 8 square feet then total 12 cans of paint will susie need to cover the whole wall.
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x^3 - (3 + x)^2x x=4
Answer: IM NOT GOING TO ANSWER YOUR QUESTION DUDE LEARN FROM YOUR TEACHER STOP CHEATING CLEARLY YOUR NOT SMART AND YOUR GOING TO FAIL YOU MATH CLASS AND EVERY OTHER SUBJECT HAHAHAHAHAHAHAHAHHAHAHAHHAHAHAHAH
Order these numbers from least to greatest: 3.4 ,7 ,-3.5 ,-3
Answer: -3.5, -3, 3.4, 7
Step-by-step explanation: If you put it on a number line, this would be the order these integers go in!