Answer:
(0, 2)
Step-by-step explanation:
The graph of g(t)= -(t-1)^2+5 is an inverted parabola with vertex at (1, 5).
Making a table of t and g values would be helpful here:
t g(t) = -(t - 1)^2 + 5
------ -----
2 4
0 4
-1 1
1 5
We're looking for an interval on which the average rate of change is zero.
Note that this is the case on the interval (2, 4); g(0) = g(2) = 4, so the change in g is 4 - 4, or zero (0).
The average rate of change of [tex]g(t)=-(t-1)^2+5[/tex] is 0 in interval [tex]-1\leq t\leq 3[/tex].
Given,
[tex]g(t)=-(t-1)^2+5\\[/tex].
We have to find the interval in which [tex]g(t)=-(t-1)^2+5\\[/tex] have an average rate of change of zero.
We know that, the function [tex]f(x)[/tex] will have average range of 0 when [tex]f(b)=f(a)[/tex].
Now we calculate g(1), g(2),g(3) and g(-1),
[tex]g(1)=-(1-1)^2+5\\g(1)=5[/tex]
[tex]g(2)=-(2-1)^2+5\\g(2)=-1+5\\g(2)=4[/tex]
[tex]g(3)=-(3-1)^2+5\\g(3)=-4+5\\g(3)=1[/tex]
[tex]g(-1)=-(-1-1)^2+5\\g(-1)=-4+5\\g(-1)=1[/tex]
Since,
[tex]g(3)=g(-1)=1[/tex] so the function [tex]g(t)=-(t-1)^2+5\\[/tex] has an average rate of zero at [tex]-1\leq t\leq 3[/tex].
For more details follow the link:
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what is this answer 4\5+2\10
Answer:
1
Step-by-step explanation:
To add fractions, we need to make the denominators the same. Luckily, we can simplify 2/10 to 1/5. Now that the denominators are both 5, we can add. When adding fractions, we only add the numerator, and the denominator remains the same, so we'd do 4+1/5, which equals 5/5, which simplifies to 1.
Answer:
1 or 10/10
Step-by-step explanation:
Step 1 make a common denominator
to make a common demoniator multiply the top and bottom number by the same number
so multiply the 4 and 5 by 2 to get 8/10
Step 2 now that you have 8/10 add it with 2/10
Step 3 solve to get 10/10 and then simplify it to 1
A professional football prospect runs 40 yards dash in 5 seconds. What is the player's average speed over this distance
Answer:
average speed = 8y/s
Step-by-step explanation:
What is the player's average speed over this distance ?Formula
s = d/t
d = 40 yards
t = 5 seconds
s = 40y/5s
= 8y/s
Which set of angle measures could be the interior angles of a triangle? Explain why 1) 90°, 90°,90° 2)80°,80°,200° 3)40°,50°,60° 4)15°,30°,135°
Answer: option 4) 15°, 30°, 135°
Step-by-step explanation: because the triangle angle rule says that all the intererior angles of the triangle sum upto 180° always
Answer:
4) 15°,30°,135°
Step-by-step explanation:
The interior angles of a triangle will add up to 180°, so we have to choose an answer choice with angles that all add up to 180.
Answer #4 is correct because 15 + 30 + 135 = 180.
A rectangle has an area of 524.4m2. One of the sides is 6.9m in length. Work out the perimeter of the rectangle. PLEASE ANSWER!!! SOON ASAP
Answer:
165.8 mSolution,
Area of rectangle= 524.4 m^2
Length(L)= 6.9 m
Breadth(B)=?
Now,
[tex]area = length \times breadth \\ or \: 524.4 = 6.9 \times b \\ or \: 524.4 = 6.9b \\ or \: b = \frac{524.4}{6.9} \\ b = 76 \: m[/tex]
Again,
Perimeter of rectangle:
[tex]2(l + b) \\ = 2(6.9 + 76) \\ = 2 \times 82.9 \\ = 165.8 \: m[/tex]
Hope this helps...
Good luck on your assignment.....
Answer:
The perimeter of the rectangle is 165.8cm
Step-by-step explanation:
Area of a rectangle = length × width
Area = 524.4m²
length = 6.9m
524.4 = 6.9 × width
width = 524.4 / 6.9
width = 76m
Perimeter of a rectangle =
2(length ) + 2(width)
length = 6.9m
width = 76m
Perimeter = 2( 6.9) + 2(76)
= 13.8 + 152
The final answer is
= 165.8cm
Hope this helps you
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 2−x and y = 4x + 3 intersect are the solutions of the equation 2−x = 4x + 3. (4 points) Part B: Make tables to find the solution to 2−x = 4x + 3. Take the integer values of x only between −3 and 3. (4 points) Part C: How can you solve the equation 2−x = 4x + 3 graphically? (2 points) PLez Answer 50 points
Answer:
Step-by-step explanation:
Part A:
We have two lines: y = 2 - x and y = 4x + 3 . Given two equations that are both required to be true. The answer is the points where the lines cross, this means we have to make the equations equal to each other. It will look like this:
2 - x = 4x + 3
Part B:
In order to solve the equation we need to put the like terms together. So we will add x on each side.
2 - x = 4x + 3
+x +x
So now we get:
2 = 5x + 3
Now that x is on one side and is positive we will move 3 on the left side by subtracting it from each side.
2 = 5x + 3
-3 -3
So now we get:
-1 = 5x
Now that the like terms have been combined we need to find out what x alone is so we divide 5 on each side:
[tex]\frac{-1}{5}[/tex] = [tex]\frac{5x}{5}[/tex]
No we see that:
x = [tex]-\frac{1}{5}[/tex]
If A=2+i, O=-4, P=-i, and S=2+4i, find A-O+P+S.
==================================================
Work Shown:
A = 2+i
O = -4, this is the letter 'oh' not to be confused with the number zero
P = -i
S = 2+4i
A-O+P+S = (2+i) - (-4) + (-i) + (2+4i)
A-O+P+S = (2+i) + 4 + (-i) + (2+4i)
A-O+P+S = (2+4+2) + (i-i+4i)
A-O+P+S = 8+4i
can some body help me plz
Answer:
Length of each side of the square = 8 cm
Step-by-step explanation:
In the figure attached, diagrams of a right triangle and a square have been given.
"Area of the square is twice the area of the triangle."
Let one side of the square = x cm
Therefore, area of the square = x²
Area of the given triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(16)(4)[/tex]
= 32 cm²
Therefore, x² = 2 × 32
x² = 64
x = 8 cm
Therefore, length of each side of the square will be 8 cm.
Find the interquartile range (IQR) of the data in the dot plot below. chocolate chips 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10. Number of chocolate chips. Chocolate chips in different cookies in a package
*The dot plot is shown in the attachment below
Answer:
2
Step-by-step explanation:
Interquartile range is the difference between the upper median (Q3) and the lower median (Q1).
First, let's write out each value given in the data. Each dot represents a data point.
We have:
2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 7
=>Find the median:
Our median is the middle value. The middle value is the 6th value = 4
==>Upper median Q3) = the middle value of the set of data we have from the median to our far right.
2, 3, 3, 4, 4, |4,| 4, 5, [5], 6, 7
Our upper median = 5
==>Lower median(Q1) = the middle value of the data set we have from our median to our far left.
2, 3, [3], 4, 4, |4,| 4, 5, 5, 6, 7
Lower median = 3
==>Interquartile range = Q3 - Q1 = 5-3 = 2
Answer:
2
Step-by-step explanation:
There are 200 people in a cinema. 25% of the people are men. 1⁄5 of the people are women. The rest of the people are children. Work out how many children are in the cinema.
Answer:
110
Step-by-step explanation:
There are 200 people in a cinema- This is our total amount.
25 % of the people are men.
.25 times 200= 50
There are 50 men.
1/5 (20%) of the people are women.
.2 times 200 = 40
There are 40 women.
50+40 = 90
There are 90 adults in the cinema.
If there are 200 total people in the cinema, and 90 of them are adult, then 110 of them are children.
The percentage is 55%.
The simplified fraction is 11/20.
The decimal is .55
12
y= x2 + x-2
x+ y=1
If (x, y) is a solution of the system of equations
above, which of the following is a possible value of
xy?
A) 7
B 1
C) -1
D) -12
Answer:
D,xy=-12
Step-by-step explanation:
y=x²+x-2
x+y=1
or x+x²+x-2=1
x²+2x-3=0
x²+3x-x-3=0
x(x+3)-1(x+3)=0
(x+3)(x-1)=0
either x=-3
or x=1
when x=-3
x+y=1
-3+y=1
y=1+3=4
one solution is (-3,4)
xy=-3×4=-12
if x=1
1+y=1
y=0
second solution is (1,0)
xy=1×0=0
Which statements are true regarding the diagram? Check all that apply.
The side opposite the 60° angle has a length of
The side opposite the 60° angle has a length of .
sin(60°) =
sin(60°) =
The other acute angle of the triangle is 30°.
Answer:
A. The side opposite the 60° angle has a length of √3/2
C.Sin(60°)=√3/2
E.The other acute angle of the triangle is 30°
Step-by-step explanation:
The diagram has been attached to the answer
A. The side opposite the 60° angle has a length of
B. The side opposite the 60° angle has a length of .
C. sin(60°) =
D. sin(60°) =
E. The other acute angle of the triangle is 30°.
Answer
The side opposite the 60° angle has a length of the square root of 3/2
Opposite side of the 60° angle has a length of √3/2
sin(60°) = the square root of 3/2
Sin(60°)=√3/2
The other acute angle of the triangle is 30°
Proof:
Total angle in a triangle=180°
180°-60°-90°
=30°
Answer:
A, D, E
Step-by-step explanation:
I do is big smart
A can in the shape of a cylinder has a diameter of 6 centimeters and a height of 10 centimeters. Which measurement is closest to the total surface area of the can in square centimeters? 245.04 cm2 203.19 cm2 376.99 cm2 188.50 cm2
Answer:
245.04 cm²
Step-by-step explanation:
Use the formula for the surface area of a cylinder: 2[tex]\pi[/tex]r² + 2[tex]\pi[/tex]rh
Now, we can plug in the values:
2[tex]\pi[/tex](3)² + 2[tex]\pi[/tex](3)(10)
18[tex]\pi[/tex] + 60[tex]\pi[/tex] = 245.04
The total surface area of the can is 244.92 square centimeters which is closest to 245.04 square centimeters.
We have a can in the shape of a cylinder has a diameter of 6 centimeters and a height of 10 centimeters.
We have to determine total surface area of the can in square centimeters.
What is the formula to calculate the total surface area of a cylinder with radius 'r' and height 'h'.The total surface area of a cylinder with radius 'r' and height 'h' is given by -
A = 2πr(h + r)
According to the question, we have -
diameter of can = 6 cm
Then, the radius will be (r) = 6/2 = 3 cm
Height of can (h) = 10 cm
Substituting the values, we get -
A = 2 x 3.14 x 3 (10 + 3)
A = 2 x 3.14 x 3 x 13
A = 6 x 13 x 3.14
A = 78 x 3.14
A = 244.92 square centimeters.
Hence, the total surface area of the can is 244.92 square centimeters which is closest to 245.04 square centimeters.
To solve more questions on Surface area of cylinder, visit the link below-
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Help !!!! Match the written mathematical operation to the equivalent symbolic form
Answer:
The matched pairs are:
(A, 4), (B, 1), (C, 2) and (D, 3)
Step-by-step explanation:
The complete question is:
Match each description of an algebraic expression with the symbolic form of that expression :
A. 2 terms; variables = x and y
B. 3 terms; variables = x and y; constant = 3
C. 2 terms; variable = x; constant = 4.5
D. 3 terms; variables = x and y; constant = 2
1. x - 2y + 3
2. 4.5 - 2x
3. 4.5x + 2 - 3y
4. 4.5y - 2x
Solution:
A. 2 terms; variables = x and y ⇒ 4. 4.5y - 2x
B. 3 terms; variables = x and y; constant = 3 ⇒ 1. x - 2y + 3
C. 2 terms; variable = x; constant = 4.5 ⇒ 2. 4.5 - 2x
D. 3 terms; variables = x and y; constant = 2 ⇒ 3. 4.5x + 2 - 3y
If the number of bacteria in a colony doubles every 10 hours and there is currently a population of 300 bacteria, what will the population be 20 hours from now?
Answer:
1200 bacteria
Step-by-step explanation:
20 hours divided by 10 hours = 2, so it will be doubled two times.
300 times 2 for the first doubling = 600
600 times 2 for the second doubling = 1200
In 2008 a newspaper sold 120 thousand papers, and had 60 thousands people reading online. Their online readership has been increasing by 8 thousand people each year, while their physical paper sales have decreased by 6 thousand papers a year. In what year does online readership exceed physical sales?
Answer:
t = 5 years
online readership will exceed physical sales in 5 years
Step-by-step explanation:
The number of physical readership can be represented by the equation;
P(t) = 120 - 6t
The number of Online readership can be represented by the equation;
K(t) = 60 + 8t
For online readership to exceed physical sales
K(t) > P(t)
60 + 8t > 120 - 6t
Collecting the like terms;
8t+6t > 120-60
14t>60
t > 60/14
t > 4.29
To the nearest year greater than 4.29.
t = 5 years
online readership will exceed physical sales in 5 years
Find the area of a trapezoid with bases of 5 feet and a 7 feet, and a height of 3 feet a. 18 b. 36 c. 72 d. 40
Answer:
The answer is option A. 18Step-by-step explanation:
Area of a trapezoid = 1/2(a + b) × h
where
h is the height
a and b are the other sides
From the question
h = 3 feet
a = 5 feet
b = 7 feet
Area = 1/2(5+7) × 3
= 1/2 ( 12) × 3
= 6 × 3
The answer is
= 18
Hope this helps you.
A Rosa le gusta jugar con su primo Eduardo utilizando números. Rosa le planteó encontrar dos números que sumados den 15 y que el doble de uno de ellos sea igual al otro más 3 unidades, ¿De qué números se trata?
Answer:
Los números son 6 y 9
Step-by-step explanation:
Este problema se puede resolver por medio de un sistema de ecuaciones.
El primer número será x y el segundo número será y.
Sabemos que los dos números suman 15, por lo tanto esto se puede escribir como:
[tex]x+y=15[/tex]
Por otro lado sabemos que el doble de uno de ellos es igual al otro más 3 unidades, esto lo podemos escribir de la siguiente manera:
[tex]2x=y+3[/tex] (el doble del primero es igual al segundo más 3)
Reescribiendo esta segunda ecuación tenemos:
[tex]2x-y=3[/tex]
Por lo tanto, nuestras dos ecuaciones son:
[tex]x+y=15\\2x-y=3[/tex]
Resolviendo el sistema por el método de reducción observamos que, si sumamos ambas ecuaciones, las y se cancelan y quedamos con:
[tex]3x=18\\x=6[/tex]
Ahora, sustituimos este valor en la primera ecuación para obtener el valor de y:
[tex]x+y=15\\6+y=15\\y=15-6\\y=9[/tex]
Por lo tanto, los números son 6 y 9
Por medio de un sistema de ecuaciones, hay qué los números son 6 y 9.
Los números son desconocidos, por lo tanto, llaremos un de x, otro de y.Los números sumados den 15, o sea:
[tex]x + y = 15[/tex]
El doble de uno de ellos sea igual al otro más 3 unidades, o sea:
[tex]2x = y + 3[/tex]
[tex]y = 2x - 3[/tex]
Reemplazando en la primera ecuación:
[tex]x + y = 15[/tex]
[tex]x + 2x - 3 = 15[/tex]
[tex]3x = 18[/tex]
[tex]x = \frac{18}{3}[/tex]
[tex]x = 6[/tex]
[tex]y = 2x - 3 = 2(6) - 3 = 12 - 3 = 9[/tex]
Los números son 6 y 9.
Un problema similar es dado en https://brainly.com/question/24646137
explain how to solve 2x+9=15
Answer:
I hope it will help you :)
Can someone help me with this question please?
Answer:
If the ratio of edge lengths is 3:5, I'm going to assume that the perimeters are going with the same ratio.
Therefore, the ratio would be 345:575.
Hope this is right and helps :)
Is 540171 divisible by 9?
Image is attached below.
If the sum of the digits its divisible by 9,
then the original number is divisible by 9.
Since 18 (the sum of the digits) is divisible by 9,
the number 540,171 is also divisible by 9.
Answer:
Yes, The number is divisible by 9
Step-by-step explanation:
If you divide the number by 9 you will get 60019. Also if we add the numbers we will get 18 which is also divisible by 9.
Hope this helps.
Which of the following are solutions to the quadratic equation? Check all that
apply.
2x2 + 7x- 14 = x2 + 4
Answer:
[tex]\boxed{\sf \ \ \ x=-9 \ \ or \ \ x=2 \ \ \ }[/tex]
Step-by-step explanation:
hello,
[tex]2x^2+7x-14=x^2+4\\<=> 2x^2+7x-14-x^2-4=0\\<=> x^2+7x-18=0\\<=>x^2-2x+9x-18=0\\<=> x(x-2)+9(x-2)=0\\<=> (x+9)(x-2)=0\\<=> x+9 = 0 \ \text{or} \ x-2=0\\<=> x = -9 \ \text{or} \ x=2[/tex]
hope this helps
An archeologist in Turkey discovers a spear head that contains 27% of its original amount of C-14
Answer:
it is 13093 i got it correct
find the value of x in the isoscleles triangle sqrt45 and altitude 3
Answer:
[tex]c.\hspace{3}x=12[/tex]
Step-by-step explanation:
Isosceles triangles are a type of triangles in which two of their sides have an identical length. It should be noted that the angles opposite the sides that are the same length are also the same. This means that these triangles not only have two equal sides, but also two equal angles.
You can solve this problem using different methods, I will use pythagorean theorem. First take a look at the picture I attached. As you can see:
[tex]x=2a[/tex]
And we can find a easily using pythagorean theorem:
[tex](\sqrt{45} )^{2} =3^{2} +a^{2}[/tex]
Solving for a:
[tex]a^{2} =(\sqrt{45} )^{2} -3^{2} \\\\a^{2} =45-9\\\\[/tex]
[tex]a^{2} =36\\\\a=\sqrt{36} \\\\a=6[/tex]
Therefore:
[tex]x=2a\\\\x=2(6)\\\\x=12[/tex]
The graph of the parent function f(x) = x3 is translated to form the graph of g(x) = (x − 4)3 − 7. The point (0, 0) on the graph of f(x) corresponds to which point on the graph of g(x)?
Answer:
The point (0, 0) in the graph of f(x) corresponds to the point (4, -7) in the graph of g(x)
Step-by-step explanation:
Notice that when we start with the function [tex]f(x)=x^3[/tex], and then transform it into the function: [tex]g(x)=(x-4)^3-7[/tex]
what we have done is to translate the graph of the function horizontally 4 units to the right (via subtracting 4 from the variable x), and 7 units vertically down (via subtracting 7 to the full functional expression).
Therefore, the point (0, 0) in the first function, will now appeared translated 4 units to the right (from x = 0 to x = 4) and 7 units down (from y = 0 to y = -7).
then the point (0, 0) after the translation becomes: (4, -7)
Answer:4, -7
Step-by-step explanation:
Solve this a² ÷ a⁴ × a²
Step-by-step explanation:
a^4 - a^4 = (a^2 +a^2)(a^2-a^2)
a^4 - a^4 = (a^2 + a^2)(a+a)(a-a)
there is no need of this solution, because it equal to 0 because a^4 - a^4 will be equal then it will be 0
i hope this will help you
Answer:
Hello There!
~~~~~~~~~~~~~~~
a² ÷ a⁴ × a² =
1
Step-by-step explanation: Simplify the expression.
Hope this helped you! Brainliest would be nice!
☆_____________❤︎______________☆
What is the solution to this equation?
4x-3 + 2x= 33
O A. x= 15
B. x = 18
O c. x = 5
O D. x = 6
Answer:
4x – 3 + 2x = 33
6x = 36
x = 6
D. x = 6
Which of the following expressions are equivalent to -9/6?
the correct answer is:
A. 9/-6
expand the following 4 (x - 1)
Answer:
4x - 4
Step-by-step explanation:
4 × x = 4x
4 × -1 = -4
4x - 4
Answer:
4x-4
Step-by-step explanation:
4(x-1) 4*x-1*44x-4A football field is a rectangle 48m wide and 91m long. The coach asks players to run diagonally across the field. How far did the players run?
Answer:
102.88 m
Step-by-step explanation:
Pythagorean Theorem:
a²+b²=c²
48²+91²=c²
2304+8281=10585
c²=10585
Square both sides
c= 102.88
How far the players ran:
102.88 m
the total surface area of a cube is 294cm2. work out the volume of the cube.
Answer: 343 cm³
Step-by-step explanation:
The surface area of a cube is 6s^2, where s is the side length of a square. Thus, first do 294/6 to get 49. Then take the square root of 49 to get that each side of the cube is 7. The volume of a cube is s^2, so simply do 7*7*7 to get that the volume of the cube is 343cm^3
Hope it helps <3
Answer:
V =343 cm^3
Step-by-step explanation:
The surface area of a cube is given by
SA = 6s^2 where s is the side length
294 = 6s^2
Divide by 6
294 / 6 = s^2
49 = s^2
Take the square root of each side
sqrt(49) = sqrt(s^2)
7 =s
The volume of a cube is
V = s^3
V = 7^3
V =343 cm^3