Answer: b=-3+2√3/2
-3-2√3/2
Step-by-step explanation: it's A on edg
The value of b which satisfies the given quadratic equation is both: A. b = (-3 + 2√3)/2 and (-3 - 2√3)/2.
How to solve a quadratic equation?
In this exercise, you're required to solve for the value of b which satisfies the given quadratic equation. Thus, we would simplify the quadratic equation as follows:
3(2b + 3)² = 36
Dividing both sides by 3, we have:
(2b + 3)² = 12
Taking the square root of both sides, we have:
2b + 3 = ±√12
2b + 3 = ±√4 × √3
2b + 3 = ±2√3
2b = -3 ± 2√3
b = (-3 + 2√3)/2 and (-3 - 2√3)/2.
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Isabella filled a 200-litter pool and Henry filled a 250-litter pool. They both started at the same time.
The following equation gives the volume of water in Isabella's pool (in liters) as a function of time (in minutes).
V=23t
The graph of the volume of water in Henry's pool (in liters) as a function of time (in minutes) is shown below.
Who filled their pool at a faster rate?
Who filled their entire pool first?
Answer:
B. Henry for the first one and A. Isebella for the second one
Step-by-step explanation:
Answer:
1. Henry
2. Isabella
Step-by-step explanation:
Game 1 gives you 200 points every time you
score. Game 2 doubles your points every time you
score (2, 4, 8, and so on). In which game do you
think you will you earn more points?
While Game 1 offers a steady 200 points per score, Game 2's point doubling system will eventually surpass Game 1's linear growth, leading to higher earnings in Game 2 over time.
To decide in which game you will earn more points, let's consider the point growth in both games. In Game 1, you receive a constant 200 points every time you score. This represents a linear growth.
However, in Game 2, your points double every time you score, starting from 2 points (2, 4, 8, 16, and so on).
This is an example of exponential growth.When comparing linear growth to exponential growth, exponential growth will eventually outpace linear growth. Initially, Game 1 will give you more points (as 200 is greater than 2, 4, 8).
However, after a certain number of scores, Game 2 will start to give you more points per score. Once you've doubled a few times, the number of points you earn in Game 2 will surpass the constant 200 points reward of Game 1.
what is the measure of CED?
An object is thrown straight up from the top of a 100-foot platform at a velocity of 48 feet per second. The height h(t) of the object t seconds after being thrown is given by [tex]h(t)=-16t^{2}+48t+100[/tex]. Find the maximum height reached by the object and the time it takes to achieve this height.
Answer:
The maximum height is 136 ftThe time it takes to achieve this height is 1.5 s.Explanation:
1. Function for the height (given):
[tex]h(t)=-16t^2+48t+100[/tex]
2. Type of function
That is a quadatic function, whose graph is a parabola that opens downward.
The maximum of the function, i.e. the maximum height, is the vertex of the parabola.
The vertex of a parabola with the genral equation [tex]y=ax^2+bx+c[/tex] is at the x-coordinate
[tex]x=-b/(2a)[/tex]
3. Time to achieve the maximum height
Substitute b with 48 and a with - 16:
[tex]t=-48/(2(-16))=48/32=3/2=1.5[/tex]
Then, time when the object achieves the maximum height it 1.5s
4. Maximum height:
Replace t with 1.5 in the equation, to find the maximum height, h(1.5)
[tex]h(1.5)=-16(1.5)^2+48(1.5)+100=136[/tex]
Then, the maximum height is 136 ft
this partial Circle has a radius of 11 in what is the area of this figure use 3.14 for pi enter your answer as a decimal in the Box round your answer to the nearest hundredth
Answer:
190 square inch
Step-by-step explanation:
Area of the partial circle = 1/2 pi r^2
Pi = 3.14
Radius r = 11 inch
Area = 1/2 x 3.14 x (11)^2
= 1/2 x 3.14 x 11 x 11
Multiply through
= 3.14 x 11 x 11 /2
= 379.94/2
= 189.97
= 190 square inch
A can of mixed nuts has 5 peanuts for every 2 cashews. There are 175 peanuts in the can .How many cashews are there ?
Step-by-step explanation:
ratio
peanuts to cashews is 5:2
so
5:2
175:?
175/5 is 35
so both side times by 35
35 X 2 is 70 cashews
Answer:
There would be 70 cashews if there are 175 peanuts.
HELP PLEASE!!I can't answer
Answer: 15%
Step-by-step explanation:
the percent is equal to (large double Cheeseburgers/total burgers) * 100
finding values
num of large double cheeseburgers in the table = 60
total burgers by adding all the values up = 68+77+45+98+52+60 = 400
calculating percent
so the percent is (60 / 400) * 100 = 15%
Solve x - 6 = 3 Question 3 options: x = 3 x = 2 x = 9 x = -3
Answer:
x = 9
Step-by-step explanation:
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
x-6-(3)=0
Step by step solution :
Step 1 :
Solving a Single Variable Equation :
1.1 Solve : x-9 = 0
Add 9 to both sides of the equation :
x=9
brainly pleasse :)
Answer:
x = 9
Step-by-step explanation:
x - 6 = 3
Add 6 to both sides
x - 6 + 6 = 3 + 6
x = 9
I hope this was helpful, please mark as brainliest
Divide: −96 ÷ −12 = A) −8 B) −7 C) 6 D) 8
Answer:
The answer is D
Step-by-step explanation:
Answer: 8, option D is correct
Step-by-step explanation:
In solving this problem, bear in mind that negative and negative gives positive as a mathematical rule, therefore, for this question, - ÷ - will give +
-96 ÷ -12
= 8
I hope this helps.
How long will it take you to
drive 120 mles at a speed of
15 miles per hour?
Answer:
8 hours
Step-by-step explanation:
you divide the miles by the miles per hour
120/15
8
Answer:
8 hours
Step-by-step explanation:
We know that
distance = rate * time
120 miles = 15 miles per hour * time
Divide each side by 15
120/15 = 15/15 *t
8 = t
It will take 8 hours
a fair charges an admisson fee for $8. Each ride is an addition $2. he equation y=8+2x describes the total x charge for y. Graph it
Answer:
When graphing in this problem we will be graphing the equation y=2x+8, where the 2x represents the fee for each ride, and 8 represents the fee to get in.
When graphing y=2x+8, you 8 is where it is going to be on the y-intercept, so the first step is to put a dot on the 8 on the y-axis. Then from that point (y-intercept) you would go up 2 and over 1, because that is your slope (2x), then you continue on with your slope up 2 and over 1, until you reach the top of your graph.
Hope this helps ;)
50% shaded? Grid
67%
33%
32%
To find the percentage shaded on the grid, count the number of shaded squares and divide it by the total number of squares.
Explanation:To find the percentage shaded on the grid, we need to count the number of shaded squares and divide it by the total number of squares. Based on the given information, we have:
67% shaded33% shaded32% shadedSince the question asks us to find the percentage shaded, the correct answer would depend on the specific grid or diagram being referred to. Without additional context or information, it is not possible to give a single definitive answer.
For which value of x is the row in the table of values incorrect
Answer:
x = 2 is incorrect
Step-by-step explanation:
The answer should be 3 instead of 4
What is the probability of selecting an even number, if you choose a number randomly {4, 10, 6, 9, 2, 14}
Approximately 67% there are 6 numbers and 4 of them are even So you have to divide 100 and 6 then multiply the answer by 4
What are the minimum and maximum values of t for which |t + 3| ≤ 2
Answer:
Max value for t is -1 and minimum value for t is -5
Step-by-step explanation:
Make two inequalities in regards to absolute value and solve both for t:
t+3<=2 and t+3>=-2
t<=-1 and t>=-5
The compound inequality would be -1>=t>=-5
Solving the absolute value inequality, it is found that:
The minimum value is t = -5.The maximum value is t = -1.-----------------
The absolute value measures the distance of a point to the origin.The inequality [tex]|f(x)| \leq a[/tex] represents the set of values of x for which the distance of points f(x) and the origin are at most a. The solution is:[tex]-a \leq f(x) \leq a[/tex]
In this problem, the inequality is:
[tex]|t + 3| \leq 2[/tex]
Thus, the solution is:
[tex]-2 \leq t + 3 \leq 2[/tex]
[tex]-2 \leq t + 3[/tex]
[tex]t + 3 \geq -2[/tex]
[tex]t \geq -5[/tex]
[tex]t + 3 \leq 2[/tex]
[tex]t \leq -1[/tex]
Then:
The minimum value is t = -5.The maximum value is t = -1.A similar problem is given at https://brainly.com/question/24005819
A square has a perimeter of 20 cm. A new square is
created that has double the perimeter of the original
square. How does the area of the new square
compare to the area of the original square?
The area quadrupled. If the original square's perimeter is 20, each side length must be 5. The new square has double the perimeter, so it's 40. This means each side of the new square must be 10.
The formula for area in a square is base x height.
Square 1 area: 5x5 = 25
Square 2 area: 10x10 = 100
100/25 is 4, so the original square's area is 4 times smaller than the new square.
A certain game has a deck of cards labeled 1,2,3, or 4. At the beginning of a turn, a player draws a card from the deck and then moves the number of spaces indicated by the number on the card. The table shows the number of each type of card in the deck. What is the expected value of the number on a card drawn from the deck.
Number on card = number of cards
1 / 20
2 / 15
3 / 10
4 / 5
A) 1
B) 2
C) 3
D) 4
Answer:
Step-by-step explanation:
1/20
F(x) =-x+1, Evaluate f(x+h)
Answer:
-1
Explanation:
Find components of the definition.
[tex]f(x+h)=-h-x+1\\f(x)=-x+1[/tex]
Plug in components
[tex]\frac{f(x+h)-f(x)}{h} = \frac{-h-x+1-(-x+1)}{h}[/tex]
Simplify.
-1
y=x+2
-3x + 3y = 6
How many solutions can be found for the system of linear equations represented on the graph?
no solution
one solution
two solutions
infinitely many solutions
The system of linear equations represented on the graph has infinitely many solutions.
Explanation:To determine the number of solutions for the system of linear equations, we can start by solving the equations. We can solve the first equation for y to get y = x + 2. We can substitute this expression for y into the second equation and then solve for x. By substituting y = x + 2 into -3x + 3y = 6, we get -3x + 3(x + 2) = 6. Simplifying this equation gives us -3x + 3x + 6 = 6, which simplifies further to 6 = 6. This equation is always true, which means there are infinitely many solutions for the system of linear equations. The two equations represent the same line, and any point on this line is a solution to the system.
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4.2 +3+2+7
Combining like terms
Answer:
16.2
Step-by-step explanation:
Add the numbers together
1. What is the value of h? (1 point)
04
O 8 square root 3
016
O8square root 2
Answer:
D) 8sqrt(2)
Step-by-step explanation:
h² = 8² + 8²
h² = 2(8²)
h = 8sqrt(2)
Solve the division problem. Round answer to the nearest hundredth. 9.2 divided by52.063
Answer: 0.18
Step-by-step explanation:
A line with a slope of 8 passes through the points (9,v) and (8,2). What is the value of v?
Answer:
Step-by-step explanation:
Given that,
Slope of line is 8
m=8
And we are given two points where the line pass through
(x1,y1) = (9,v). ; x1=9, y1=v
(x2,y2)= (8,2). ; x2=8, y2=2
The slope of a line is given as
m=∆y/∆x
m=(y2-y1)/(x2-x1)
8=(2-v)/(8-9)
8=(2-v)/(-1)
Cross multiply
8×-1=2-v
-8=2-v
Subtract 2 from both sides
-8-2=2-v-2
-10=-v
Divide both sides by -1
-10/-1=-v/-1
Note, -÷-=+
10=v
Then v=10
We can write this as an expression:
[tex]\frac{2-v}{8-9}=8[/tex] → [tex]\frac{2-v}{-1}=8[/tex]
Now, lets solve for v.
[tex]\frac{2-v}{-1}=8[/tex]
~Multiply -1 to both sides
[tex]\frac{2-v}{-1}[/tex] * -1 = 8 * -1
~Simplify
2 - v = -8
~Subtract 2 to both sides
2 - 2 - v = -8 - 2
~Simplify
-v = -10
~Divide -1 to both sides
-v/-1 = -10/-1
~Simplify
v = 10
Best of Luck!
PLEASE HELP!!
What transformation can you use to obtain the graph of f(x)=(1/2)^x from the graph of f(x)=2^x?
Answer:
[tex]f(x) = 2^{-x}[/tex]
Step-by-step explanation:
The transformation is a reflection across the y-axis
A reflection across the y-axis is produced by putting a negative sign in front of the x.
Which expression gives the value of x?
A) 15 tan30°
B) 15 cos30°
C)
15
tan30°
D)
15
sin30°
Answer:
a is correct
Step-by-step explanation:
A city council member wanted to know how his constituents felt about a planned rezoning. He randomly selected 150 names from the city phone directory and conducted a phone survey. Identify the population and sample for this situation. A) The population is residents of the city; the sample is the registered voters in the city. B) The population is everyone listed in the city phone directory; the sample is registered voters in the city C) The population is registered voters in the city; the sample is everyone listed in the city phone directory. D) The population is everyone listed in the city phone directory; the sample is the 150 people selected.
Answer:
it is D
Step-by-step explanation: it just is i did it on usa test prep
True or False: a = 6 is a solution to the inequalty a > 6.
Answer:
False
Step-by-step explanation:
If you do a = 6, then you get 6 > 6 which is not true. 6 isn't greater than itself.
Answer:
False
Step-by-step explanation:
Your inequality shows that a is greater than 6, thus meaning can not equal 6.
Show work and and answer.
18a. 5-2(x-1)=12
B. 5+2 (x-1)=12
C. 5-2 (x+2)=12
D. 5-2x +2 =12
Answer:
Step-by-step explanation:
5-2(x-1)=12
5-2x+2=12
5+2-2x=12
7-2x=12
2x=7-12
2x=-5
x=-5/2
Segments CD, AE, and BF are medians of triangle ABC.
What is the value of x?
A. x = 1.9
B. x = 2.7
C. x = 5.5
D. x = 11
Option C: x = 5.5 is the value of x
Explanation:
Given that CD, AE, an BF are the medians of the triangle ABC
Also, given that [tex]AM = 4x - 5[/tex] and [tex]ME=x+3[/tex]
We need to determine the value of x.
Since, we know that the centroid divides the median in the ratio 2 : 1
Hence, we have,
[tex]AM=2\times ME[/tex]
Substituting the values, we get,
[tex]4x-5=2(x+3)[/tex]
Simplifying, we get,
[tex]4x-5=2x+6[/tex]
Subtracting both sides of the equation by 2x, we have,
[tex]2x-5=6[/tex]
Adding both sides of the equation by 5, we have,
[tex]2x=11[/tex]
Dividing both sides of the equation by 2, we get,
[tex]x=5.5[/tex]
Therefore, the value of x is 5.5
Hence, Option C is the correct answer.
An oak tree is 12 feet tall and a bird is standing on the ground 16 feet from the tree. If the bird flies directly to the top of the tree, how far will it fly?
Answer:
20 ft.
Step-by-step explanation:
There are two different (yet similar) ways to solve this problem:
a. Pythagorean theorem
b. Pythagorean triplet recognition
With option "a", you set it up:
12² + 16² = x²
144 + 256 = x²
400 = x²
x = 20
But, the arguably "easier" way to find out the distance is to use the Pythagorean's triplet recognition.
We know that the most common right triangle is the 3-4-5 right triangle.
If you take the three side lengths, and multiple them by the same thing, those are the sides to another right triangle.
ex. 3-4-5 * 5
15-20-25 are the sides of another right triangle!
This also means that if you have a triangle that has the sides 15, 20, and 25, you immediately know it's a right triangle.
When we look at 12 and 16, we know they are the legs of the triangle.
We also know that if we multiply 4 times 3 and 4, it will equal 12 and 16.
So what's 5 times 4? 20!
Final answer:
To find how far the bird will fly to the top of the tree, we use the Pythagorean Theorem. By squaring the height of the tree and the distance from the bird to the tree, we find that the hypotenuse, or the distance the bird will fly, is 20 feet.
Explanation:
The question asks about the distance a bird will fly from the ground to the top of a tree, which involves the application of the Pythagorean Theorem to solve for the hypotenuse of a right triangle. The tree's height (12 feet) represents one leg of the right triangle, and the distance from the bird to the tree (16 feet) represents the other leg. To find the distance the bird flies (the hypotenuse), we use the equation:
a² + b² = c²
Where ‘a’ and ‘b’ are the lengths of the legs, and ‘c’ is the length of the hypotenuse. Now we can calculate it:
12² + 16² = c²
144 + 256 = c²
400 = c²
[tex]\sqrt{400}[/tex] = c
20 feet = c
Therefore, the bird will fly 20 feet to reach the top of the oak tree.