Answer:
[tex]\text{(h, f(h)) where h=} \dfrac{x_1+x_2}{2}\\[/tex] , ([tex]x_1,x_2,[/tex] zeros of the polynomial)
Step-by-step explanation:
Given the zeros of a polynomial, [tex]x_1\: and \:x_2[/tex], to determine the vertex, follow these steps.
Find the equation of symmetry x=h where [tex]h=\dfrac{x_1+x_2}{2}[/tex]
Substitute the value of h into the quadratic function f(x) to find the maximum of minimum point.
Therefore, the coordinate of the vertex will be:
[tex]\text{(h, f(h)) where h=} \dfrac{x_1+x_2}{2}[/tex]
At the beginning of summer, the water level on a pond is 2 feet below its normal level. After an unusually dry summer, the water level on the pond dropped another 2 feet. How far above or below the normal water level is the pond at the end of the summer?
Answer:
Step-by-step explanation:
A company usually sends 9 people to install a security system in an office building, and they do it in about 96 minutes. Today, they have only three people to do the same size job. How much time should be scheduled to complete the job?
Answer:
The Answer would be 288 minutes
Step-by-step explanation:
So we have 9 people working to install a security system in an office building. they take about 96 minutes.
Today we have 3 people doing the same job.
yesterday we had 9 people doing the same job
so we would multiply 96 minutes by 3 because we divided the amount of people by 3
96x3= 288
3 people takes 288 minutes to do the same job.
To complete the installation of a security system that normally takes 9 people 96 minutes, three people would require 288 minutes given each person works at the same rate and the work is additive.
Explanation:When a company usually sends 9 people to install a security system in 96 minutes, and today only has three people available for the same task, we need to calculate the expected time for completion. First, we assume that each person works at the same rate. With 9 people, it takes 96 minutes, so with one person, it would take 9 times longer, since the number of workers is inversely proportional to the time needed.
So, one person would take 9 × 96 = 864 minutes to do the job alone. Therefore, three people would take 864 ÷ 3 = 288 minutes to complete the installation of the security system.
This calculation is based on the assumption that the work done by each individual is additive and that they are working on the task continuously and independently without interruption.
Emilia made fewer than 27 bracelets last week. The variable b represents the number of bracelets. The inequality describes the number of bracelets that Emilia made. Which could be a solution to the inequality?
26
29
33
40
Answer:
The answer is A. 26
Step-by-step explanation:
26 is the only answer that makes sense becuase it is the only one less that 27. The answer is written as 26>27. All tho anwers dont make sense because they are less than 27.
PLUS I TOOK THE TEST
2. Vance is solving the inequality below and will represent his solution on a number line. Which of the following is NOT true about the number line Vance will create?
-7c-13<64
-
a. The number line should have a closed circle
b. The arrow will point to the left
c. The circle should be placed above -11
d. All of the above are true
Question 5:
Factor (x^2 – 9) (x^2 – 5x + 4) completely.
Answer:
I believe the answer is (x+3)(x-3)(x-4)(x-1)
Step-by-step explanation:
Notice both terms are perfect squares, therefore you can factor using the difference of squares formula:
(x²-9)(x²-5x+4)
For the first term, we get (x+3)(x-3) because x²-9 is a perfect square.
For the second term, we get (x-4)(x-1) because x²-5x+4 is a perfect square trinomial.
If you have any further questions about this problem, you can comment them down below and I'll try to answer them.
Please help !! :) 30 points.
Which could be measured in meters?
A. the weight of a whale
B. the amount of juice to buy
c. the length of a soccer field
D. the time it takes to run a mile
E. the temperature in summer
Answer:the length of a soccer field
PLZ GIVE ME BRAINLIEST
C.
Step-by-step explanation:
What is the 6th term in this geometric sequence? 5, -15, 45, -135
Answer:
-1215.
Step-by-step explanation:
For a geometric sequence:
nth term = a1 r^(n-1)
The first term a1 = 5 and the common ratio r = -15/5 = -3.
So 6th term = 5 * (-3)^(6-1)
= 5 * (-3)^5
= -1215.
The 6th term in this geometric sequence should be considered as the -1215.
Calculation of the 6th term:The following formula should be used for the same.
nth term = [tex]a_1\ r^{(n-1)[/tex]
Here,
The first term a1 = 5
and the common ratio r = [tex]-15/5[/tex]= -3.
So 6th term should be
[tex]= 5 \times (-3)^{(6-1)}[/tex]
[tex]= 5 \times (-3)^5[/tex]
= -1215
Hence, The 6th term in this geometric sequence should be considered as the -1215.
Learn more about geometric here: https://brainly.com/question/16009711
HELP A 13 YEAR OLD PLEASEEEEEEEEEEEEEEEEEE
Answer:
A and B
Step-by-step explanation:
also hey becky!
2 Points
Classify the following triangle. Check all that apply.
The given number line shows the solutions to which inequality?
A)
x + 7 ≤ 5
B)
x + 3 ≥ 1
C)
x − 5 > 2
D)
x − 1 ≤ 1
Answer:
A)
x + 7 < 5
Shows inequality
The correct inequality that represents the solutions on the given number line is C) [tex]\( x - 5 > 2 \).[/tex]
To find the correct inequality, we need to determine which one corresponds to the shaded portion of the number line. The shaded portion indicates the set of all [tex]\( x \)[/tex] values that satisfy the inequality.
Let's analyze each option:
A) [tex]\( x + 7 \leq 5 \)[/tex]
If we solve this inequality, we get:
[tex]\( x \leq 5 - 7 \)[/tex]
[tex]\( x \leq -2 \)[/tex]
This inequality would be represented by a number line shaded to the left of -2, including -2 itself. This does not match the given number line, which is shaded to the right of a point.
B) [tex]\( x + 3 \geq 1 \)[/tex]
Solving this inequality, we get:
[tex]\( x \geq 1 - 3 \)[/tex]
[tex]\( x \geq -2 \)[/tex]
This inequality would be represented by a number line shaded to the right of -2, including -2 itself. However, the inequality sign in the question is non-inclusive, which means -2 itself should not be shaded. This does not match the given number line, which has a shaded circle at the starting point of the shaded region, indicating inclusivity.
C) [tex]\( x - 5 > 2 \)[/tex]
Solving this inequality, we get:
[tex]\( x > 2 + 5 \)[/tex]
[tex]\( x > 7 \)[/tex]
This inequality would be represented by a number line shaded to the right of 7, not including 7 itself. This matches the given number line, which shows the shaded region starting just to the right of 7 (indicated by an open circle at 7).
D) [tex]\( x - 1 \leq 1 \)[/tex]
Solving this inequality, we get:
[tex]\( x \leq 1 + 1 \)[/tex]
[tex]\( x \leq 2 \)[/tex]
This inequality would be represented by a number line shaded to the left of 2, including 2 itself. This does not match the given number line, which is shaded to the right of a point and has an open circle at the starting point of the shaded region.
Therefore, the correct answer is C)[tex]\( x - 5 > 2 \)[/tex], as it accurately describes the shaded region on the given number line.
In driving down to Salem, Nathan strictly followed the speed limit. He drove 55 mph for 15 minutes in the city and then 65 mph for 25 min through the countryside.
What was Nathan’s average speed for the whole trip?
61.25MPH
55*15+65*25=2450
2450/40=61.25MPH
ANSWER IS 61.25 MPH
)) Sophie bought 6 packages of cat food and 4 packages of dog food. Each package of cat
food contained 8 cans, and each package of dog food contained 2 cans. How many more cans
of cat food than dog food did Sophie buy?
Answer:
6 x 8 = 45 cans of cat food
4 x 2 = 8 cans of cat food
45 - 8 = 37
Sophie has 37 more cans of cat food than she does of dog food
Step-by-step explanation:
Help with my homework!
Answer:
a) 72 cm2 (centimeter square)
b) 9 cm2 (centimeter square)
c) 9 cm2 (centimeter square)
d) 54 cm2 (centimeter square)
Step-by-step explanation:
a) the area of the rectangle = Base x Height
= 12 x 6
= 72 cm2 (centimeter square)
b) the area of the triangle A = 1/2 x Base x Height
= 1/2 x 3 x 6
= 9 cm2 (centimeter square)
c) the area of the triangle B = 1/2 x Base x Height
= 1/2 x 3 x 6
= 9 cm2 (centimeter square)
d) area of the parallelogram = area of the rectangle - area of triangle A - Area of triangle B
= 72 - 9 - 9
= 54 cm2 (centimeter square)
$2.95 for a notebook plus 7% tax.
I need help with this
Can you include steps please
Answer:
$3.16
Step-by-step explanation:
$2.95 + 7%= 3.1565
by rounding up you get $3.16.
Answer:
$3.16
Step-by-step explanation:
To find the total, find how much the tax is. Multiply the price of the notebook by the percentage the tax is.
$2.95 × 0.07 = $0.21
Add the value of tax with the price of the book.
$2.95 + $0.21 = $3.16
You can also solve this problem by multiplying the price of the notebook by the percentage of the tax plus one.
$2.95 × 1.07 = $3.16
ANSWER ASAP!
How many solutions does this system have?
y=3x-5
y=-x+4
one
two
an infinite number
no solution
A rectangular one story house covers an area of 3,700 square feet. The ceilings are 8 feet high. What is the volume of the interior of the house?
Answer:
29,600 feet cubed
Step-by-step explanation:
The surface area is 3700 square feet.
The house is 8 feet tall.
Simply, you just have to multiply 3700 * 8.
What is the scale factor of figure A to figure B?
Score for Question 3: ___ of 5 points)
3. Use the diagram of a REGULAR HEXAGON and follow these steps to solve for the area of a hexagon with sides equal to 4 cm. Leave radicals in your answers.
How many equilateral triangles are there? __________
If we cut an equilateral down the middle (green line) what special triangle do you create? __________
Sketch and label all side lengths of the 30-60-90 triangle by itself below.
What is the length of the short side of one 30-60-90 triangle? __________
What is the length of the hypotenuse of one 30-60-90 triangle? __________
Apply properties of 30-60-90 triangles to calculate the long leg: ¬¬¬¬___________
What is the vocabulary word for the long side of the 30-60-90 called in the polygon (green line)? ____________
What is the height of the equilateral triangle? _________
Apply triangle area formula to calculate the area of one equilateral triangle: ____________
Calculate the area of the complete hexagon by multiplying area of one equilateral triangle by # of triangles:
Answer:
(a)6 Equilateral Triangles.
(b)30-60-90 triangle.
(c)See Attached Triangle in Figure 2
(d)Length of the short leg = 2cm.
(e)Length of the hypotenuse= 4cm.
(f)Length of the long leg=[tex]2\sqrt{3}cm[/tex]
(g)Apothem.
(h)Height of the Equilateral triangle=[tex]2\sqrt{3}cm[/tex]
(i)Area of One Equilateral triangle =[tex]4\sqrt{3}cm^2[/tex]
(j)Area of Hexagon =[tex]=24\sqrt{3}\:cm^2[/tex]
Step-by-step explanation:
(a)From Figure 1, there are 6 Equilateral Triangles.
(b)If we cut an equilateral down the middle (green line), we create a 30-60-90 triangle.
(c)Triangle Attached in Figure 2.
(d)The length of the short leg of one of the 30-60-90 triangle is 2cm.
(e)The length of the hypotenuse of one of the 30-60-90 triangle is 4cm.
(f)Length of the long leg
We use Pythagoras Theorem to find the length of the long leg of the right triangle.
[tex]4^2=2^2+l^2\\l^2=4^2-2^2=12\\l=\sqrt{12}=2\sqrt{3}cm[/tex]
(g)The vocabulary word for the long side of the 30-60-90 called in the polygon (green line) is Apothem.
It is line segment from the center to the midpoint of one of the sides of a polygon.
(h)Height of the Equilateral Triangle=[tex]2\sqrt{3}cm[/tex]
(i)Area of One Equilateral triangle
Base =4 cm, Height =[tex]2\sqrt{3}cm[/tex]
Area=0.5X4X[tex]2\sqrt{3}cm[/tex]
=[tex]4\sqrt{3}\:cm^2[/tex]
(j)Area of Hexagon =Area of One Equilateral Triangle X 6
[tex]=6X 4\sqrt{3}\\=24\sqrt{3}\:cm^2[/tex]
plz answer the question
Answer:
c = 11.3 yards
Step-by-step explanation:
The area (A) of a trapezium is calculated as
A = [tex]\frac{1}{2}[/tex] h (a + b)
where h is the perpendicular height and a, b the parallel bases
Here A = 416.955, h = 20.9, a = 28.6 and b = c, thus
[tex]\frac{1}{2}[/tex] × 20.9 × (28.6 + c) = 416.955, that is
10.45(28.6 + c) = 416.955 ( divide both sides by 10.45 )
28.6 + c = 39.9 ( subtract 28.6 from both sides )
c = 11.3 yards
Please help I really need it!! Answer for both
Answer:
(-11, -4)
Step-by-step explanation:
this is the answer
13. A pilot flying over norfolk airport is told he will have to redirect and land in either richmond or raleigh. Due to air traffic, he is then told he must land in raleigh. find the distance he will travel.
- the answer is 151 miles,but I need work :)
Answer:
151 mi
Step-by-step explanation:
Considering the question given, the distance we are trying to obtain is the distance between Raleigh and Norfolk.
Steps on how to obtain the distance travel by the pilot is given in the attached photo.
Suppose a normal distribution has a mean of 26 and a standard deviation of 4. What is the probability that a data value is between 27 and 28? Round your answer to the nearest tenth of a percent.
A. 12.3%
B. 9.3%
C. 10.3%
D. 11.3%
Answer:
Answer is B. 9.3
Step-by-step explanation:
I took the test
There is a probability of 9.3% that the normal distribution data value is between 27 and 28
What is z score?The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
z = (raw score - mean)/standard deviation
Given that:
mean of 26 and a standard deviation of 4, For:
For x = 27:
z = (27 - 26) / 4 = 0.25
For x = 28:
z = (28 - 26) / 4 = 0.5
P(0.25 < z < 0.5) = P(z < 0.5) - P(z < 0.25) = 0.6915 - 0.5987 = 0.093
There is a probability of 9.3% that the normal distribution data value is between 27 and 28
Find out more on z score at: https://brainly.com/question/25638875
Plz help i will give brainliest
Answer:
$56
Step-by-step explanation:
35 percent *160 =
(35:100)*160 =
(35*160):100 =
5600:100 = 56
Answer:
$56.
Step-by-step explanation:
Since it is 35% off, we can simply take 35% of the original price:
160 × 0.35 = $56.
find the exact length of the third side
Answer:
9
Step-by-step explanation:
a triangle is bacicly half of a rectangle so 3 x 6 is 18 but since it's just half, you divide by 2 and you get 9!
Step-by-step explanation:
Phytagoras Theorem :
c² = a² + b²
c² = 3² + 6²
c² = 9 + 36
c² = 45
c = √45
So, the exact length og the third side is √45
Hope it helpful and useful :)
How do I find this?Please help!!!
Answer:
d) [tex]y=-\frac{1}{2} (x-3)^{2} -4[/tex]
Step-by-step explanation:
When you reflect an equation the slope is the opposite (if the slope is positive it'll be negative when reflected)
The slope is [tex]\frac{1}{2}[/tex] and when it is reflected it is [tex]-\frac{1}{2}[/tex]
When you shift something to the right you add [tex](x-3)^{2}[/tex]
What does this equal?
Answer:
x²y²+xy²+3+xy+2y²
Step-by-step explanation:
(2x²y²+x²y+xy²+3)-(x²y²+x²y²+x²y-xy-2y²)
1. remove the parentheses (when there’s - in front of an expression in parentheses change the sign of each term of the expression)
2x²y² + x²y + xy² + 3-x²y² - x²y² - x²y + xy - 2y²
2. eliminate the opposites
2x²y² + xy² + 3 -x²y² + xy +2y²
3. collect like terms
x²y² + xy² + 3 + xy + 2y²
Please Help. Find the value of x in the isosceles triangle shown below
Answer:
the answer is 6
Step-by-step explanation:
By pytagoras Theorem
hope its helpful
The graph shows a line and two similar triangles.
What is the equation of the line?
A) y=3x
B) y=1/3x
C) y=1/3x+2
D) y=3x+2
A bond is initially bought for $250. It doubles in value every decade.Write an equation relating v, the value of the bond, to d, the number of decades since the bond was bought.
Answer:
V=250(2d)
Step-by-step explanation:
The equation representing the value of a bond doubling every decade is
V = 2d(250).
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, A bond is initially bought for $250 and it doubles in value every decade.
Let, 'v' be the value of the bond at any given time and 'd' be the number of decades.
Therefore, The equation that represents this situation is,
V = 2d(250).
learn more about numerical expressions here :
https://brainly.com/question/29199574
#SPJ3
Find the surface area of a cylinder with a base radius of 4m and a height of 5m.
Write your answer in terms of pi, and be sure to include the correct unit.
Answer:
A≈226.19
Step-by-step explanation:
The formula is A=2πrh+2πr²
you fill in the radius and get A=2π4h+2π4²
Then fill in the height and get A=2π4×5+2π4²
and your final answer would be A≈226.19