Answer:
C. [tex]f(x) = (x-2.5)^{2}-3.25[/tex]
Step-by-step explanation:
The vertex form for a quadratic function is:
[tex]f(x) = a(x-h)^2+k[/tex]
Then, you expand the binomial and get:[tex]f(x) = a(x^2-2hx +h^2) + k[/tex]
Now you distribute and get the first form:[tex]f(x) = ax^2-2ahx +ah^2 + k[/tex]
You know that the general form for a quadratic function is:[tex]f(x) = ax^2+bx+c, Second\ form[/tex]
You compare the two forms that you have and finding h and k:[tex]ax^2+2ahx +ah^2 + k = ax^2+bx+c[/tex]
Finding h from the coefficient of X:[tex]-2ah = b[/tex]
[tex]h = -\frac{b}{2a}[/tex]
from the quadratic function given you know that a = 1 , b = -5 and c = 3, thus:
[tex]h = -\frac{(-5)}{2(1)}=2.5[/tex]
Finding k from the third coefficient:[tex]ah^2+k = c[/tex]
[tex]Isolate\ k =>\ k = c-ah^2[/tex]
You know c,a and h, so replace the values:
[tex]k = 3-(1)(2.5)^2 \\ k = 3-6.25\\ k = -3.25\\[/tex]
• Finally replace the values for a, h and k in the vertex form:
[tex]f(x) = a(x-h)^2+k\\ f(x) = (1)(x-2.5)^2+(-3.25)\\ f(x) = (x-2.5)^2-3.25[/tex]
So answer is C. [tex]f(x) = (x-2.5)^2-3.25[/tex]
factor z^2 - 3z - 18
Answer:
(z-6)(z+3)
Step-by-step explanation:
Answer:
The factored form of the given expression is (z-6)(z+3).
Step-by-step explanation:
The given expression is
[tex]z^2-3z-18[/tex]
The middle term can by written a -6z+3z.
[tex]z^2-6z+3z-18[/tex]
[tex]z(z-6)+3(z-6)[/tex]
[tex](z-6)(z+3)[/tex]
Therefore the factored form of the given expression is (z-6)(z+3).
What Is The Value Of 12 Divided By 6 2/3
Answer:9/5
Step-by-step explanation:
Hi there, hope this helps you. Have a great day! :)
Answer:
1 4/5
Step-by-step explanation:
1. Convert your mixed numbers to fractions. Your equation will become:
[tex]\frac{12}{1}[/tex] / [tex]\frac{2}{3}[/tex]
2. Apply the fractions formula for division.
[tex]\frac{12 x 3}{ 1 x 20}[/tex]
3. Solve the fraction formula for division.
You'll get [tex]\frac{36}{20}[/tex]
4. Simplify. Your final answer is [tex]1 \frac{4}{5}[/tex]
What is the probability that a vehicle is white?
Answer:
B. 0.22
Step-by-step explanation:
8/36 = 0.2222
B is the correct answer
Joy is planning to purchase a sweater that costs $30 dollars at her local department store. The sweaters are on sale for 20% off.
Which steps are needed to find the sale price of the sweater?
A. Convert the percent to its decimal equivalent. Multiply the decimal by the original amount to find the discount.
B. Convert the percent to its decimal equivalent. Divide the decimal by the original amount to find the discount. Subtract the discount from the original amount.
C. Convert the percent to its decimal equivalent. Multiply the decimal by the original amount to find the discount. Add the discount to the original amount.
D. Convert the percent to its decimal equivalent. Multiply the decimal by the original amount to find the discount. Subtract the discount from the original amount.
To find the sale price of a sweater, convert the discount percentage to a decimal, multiply by the original price to get the discount amount, and subtract this from the original price. So correct answer is B.
The correct steps needed to find the sale price of the sweater that Joy is planning to purchase are as follows:
Convert the percent discount to its decimal equivalent.
Multiply the decimal by the original amount to find the discount amount.
Subtract the discount amount from the original amount to determine the sale price.
find the product of 2 and (3.7 × 10^-4)
Answer:
74000
Step-by-step explanation:
1. 10^-4=10000
2. 10000*3.7=37000
3. 37000*2=74000
use the quadratic formula to solve the equation 4x²-x+3=0
Answer:
[tex]x=\frac{1+ \sqrt{47}i}{8}[/tex] and [tex]x=\frac{1 -\sqrt{47}i}{8}[/tex]
Step-by-step explanation:
Given quadratic equation is [tex]4x^2-x+3=0[/tex].
Compare with [tex]ax^2+bx+c=0[/tex], we get:
a=4, b=-1, c=3
Now plug these values into quadratic formula :
[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-\left(-1\right) \pm \sqrt{\left(-1\right)^2-4\left(4\right)\left(3\right)}}{2\left(4\right)}[/tex]
[tex]x=\frac{1 \pm \sqrt{1-48}}{8}[/tex]
[tex]x=\frac{1 \pm \sqrt{-47}}{8}[/tex]
[tex]x=\frac{1 \pm \sqrt{47}i}{8}[/tex]
Hence final answer is
[tex]x=\frac{1+ \sqrt{47}i}{8}[/tex] and [tex]x=\frac{1 -\sqrt{47}i}{8}[/tex]
Answer:
Solution of given quadratic equation,
x = [1 + 6.86i]/8 or x = [1 - 6.86i]/8
Step-by-step explanation:
Points to remember
Solution of a quadratic equation ax² + bx + c = 0
x = [-b ± √(b² - 4ac)]/2a
It is given a quadratic equation, 4x²-x+3=0
To find the solution using quadratic formula
Here a = 4, b = -1 and c = 3
We have,
x = [-b ± √(b² - 4ac)]/2a
x = [--1 ± √((-1)² - 4*4*3)]/2*4
= [1 ± √(1 - 48)]/8
= [1 ± √(-47)]/8
= [1 ± 6.86i]/8
x = [1 + 6.86i]/8 or
x = [1 - 6.86i]/8
Which of the following arcs are congruent in the circle below?
D) Arc wx and arc yz is the correct answer because both arcs are equal to 27
Answer:
Option D is correct.
Step-by-step explanation:
Arcs are said to be equal if it subtends equal angles at the center
here we can see that arcs WX and ZY subtends equal angle and its measure is 27 degrees.
therefore option D is correct answer
Since we are not given the angles subtended by WY and XZ in the center
so we cannot say for option A
Likewise we cannot say for rest of the option.
The mean number of catfish in all 6 samples is approximately 5.7. If 200 fish are in the pond, which proportion can be used to predict the number of catfish in the population?
Answer: There would be 190 catfish in all 200 samples in the population.
Step-by-step explanation:
Since we have given that
Number of fish = 6
Mean number of catfish = 5.7
If the number of fish = 200
So, we need to find the proportion to find the number of catfish in the population.
Let the number of catfish in the population be 'x'.
According to question, it becomes,
[tex]\dfrac{6}{5.7}=\dfrac{200}{x}\\\\6x=5.7\times 200\\\\6x=1140\\\\x=\dfrac{1140}{6}\\\\x=190[/tex]
Hence, there would be 190 catfish in all 200 samples in the population.
Answer:
A
Step-by-step explanation:
edge 2021
which function has the greatest y- intercept? A. f(x)= 3x) B. 2x+3y=12 ) C. the line that has a slope of 2 and passes through (-1,-4) D. a graph
Answer:
#4
Step-by-step explanation:
1) The y intercept is 0.
2) Convert to slope-intercept form:
2x + 3y = 12
3y = -2x + 12
y = -2/3 x + 4
So the y-intercept is 4.
3) Write in point-slope form:
y + 4 = 2 (x - 1)
Now convert to slope-intercept form:
y + 4 = 2x - 2
y = 2x - 6
So the y-intercept is -6.
4) The y-intercept is 5.
So of the four lines, #4 has the largest y-intercept.
Answer:
[tex]\boxed{\text{(4) The graph}}[/tex]
Step-by-step explanation:
The question is asking, which function has the greatest value when x = 0?
We must evaluate f(0) for each one.
(1) ƒ(x) = 3x
f(0) = 3 × 0 = 0
(2) 2x + 3y = 12
Let x = 0.
2 × 0 + 3y = 12
0 + 3y = 12
3y = 12
y = 4
(3) The line
The line has a slope of 2, and y= -4 when x = 1.
y increases by 2 when x increases by 1.
For the same reason, y decreases by 2 when x decreases by 1.
Thus, when x decreases from 1 to 0, y decreases from -4 to -6.
f(0) = -6.
(4) The graph
The graph has a y-intercept at y = 5, so,
f(0) = 5.
[tex]\boxed{\textbf{The graph}}[/tex] has the greatest y-intercept.
What's the least amount 0.146, 2.0102, 0.45, 1.09, 2.001
The least amount would be 0.146 because the tenths digits is the smallest.
The least amount among the given different amounts is 0.146
What is least amount of something?Least amount of something means the smallest amount or number.
How to find the least number or amount among the list of numbers?To find the least number or amount among the list of numbers we first go through the whole list of numbers and compare their values one after the other. And we arrange these numbers or amount in ascending order and find the least one.
According to the given question
We have different amounts
0.146, 2.0102, 0.45, 1.09, 2.001
For finding the least amount, arrange all the given amount in the ascending order.
So, the required ascending order is
0.146, 0.45, 1.09, 2.001, 2.0102
Hence, the least amount among the given different amounts is 0.146.
Learn more about least amount or number here:
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WILL GIVE BRAINLIEST, 5/5 RATING, AND LIKE!
Answer:
ok thanks :)
Step-by-step explanation:
Answer:
Sounds epic
Step-by-step explanation:
Sara has a circular fence around her dog house. Each day when she comes home from
school the dog runs exactly three laps around his pen before he is calm enough to be
petted. If the radius of his pen is 12 meters, how far does her dog run?
Answer needs to be explained
WILL GIVE BRAINLYIST
Answer:
226.2 feet
Step-by-step explanation:
The fence around the dog's house is a circle, with a radius of 12 meters.
To calculate the distance the dog runs, we need to find the circumference of that circle, which is given by the formula:
C = 2 π r, since we know r, the calculation is easy:
C = 2 π 12 = 24 π = 75.4 feet.
The dog makes three laps around the circle before calming down... so he runs 3 times 75.4 feet.
Dogs run = 3 x 75.4 ft = 226.2 feet
Chuck puts $900,000 into an account that earns 5% APR compounded annually how much money will chuck earn each year in interest
Answer:
45,000
Step-by-step explanation:
Apex is the source
Answer: the answer is $ 45,000 APEX
Two groups of workers are painting a bridge in the bay. The first group is responsible for painting the north side of the bridge, and the second group is responsible for painting the south side of the bridge. The first group has already painted 2 kilometers of the bridge and is painting 2 additional kilometers per day. The second group has already painted 5 kilometers of the bridge and is painting 1 additional kilometer per day. When the two groups have painted the same amount of the bridge, how much of the bridge will they each have painted?
Answer:
They will each have painted 8 km. This goal will be met on Day 4.
Step-by-step explanation:
Group A | Group B
Start: 2 | Start: 5 Day 1
2 + 2 = 4 | 5 + 1 = 6 Day 2
4 + 2 = 6 | 6 + 1 = 7 Day 3
6 + 2 = 8 | 7 + 1 = 8 Day 4
The first group and second group of workers will each have painted 8 kilometers of the bridge after 3 days.
Explanation:This question is related to the concept of linear equation in one variable. To solve such a problem, we typically set up an equation that relates the two groups and the amount they have painted to find out when they have painted an equal amount.
The equation representing the painting work of the first group is: 2 + 2d = x, where d is the number of days and x is the total distance painted. For the second group, the equation is 5 + d = x. We can set up these equations because each new day adds certain kilometers to the existing painted distance.
To find when these two equations are equal, we can simply equate them: 2 + 2d = 5 + d. Solving this equation, we get d = 3 days. Substituting d = 3 into either of the group's equations, we get x = 8 kilometers.
So, after 3 days, both groups would have painted 8 kilometers each.
Learn more about Simultaneous Equations here:https://brainly.com/question/31913520
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Katherine has a 30 foot length of ribbon. She cuts the ribbon into 7 pieces of equal length. The length of each piece of ribbon will fall between which two whole- number lengths?
A. 2 and 3
B. 3 and 4
C. 4 and 5
D. 5 and 6
C. 30 divided by 7 is roughly 4.3 which’s is between 4 and 5
A rectangular prism has a length of 8 in., a width of 4 in., and a height of 2 1/4 in. The prism is filled with cubes that have edge lengths of 14 in. How many cubes are needed to fill the rectangular prism? Enter your answer in the box. To fill the rectangular prism, cubes are needed.
It is not possible to fill a smaller rectangular prism with larger 14-inch cubes.
However, there is a typo in the question because the cubes with an edge length of 14 inches cannot fit inside a rectangular prism of smaller dimensions.
Hence, it is impossible to fill the rectangular prism with cubes of 14-inch edge lengths.
please help me i’m very confused
The ratio of dry rice to water is 1 to 2. This means that water is two times more than dry rice. Since the chef uses 9.5 cups of dry rice, the chef needs 19 cups of water.
You can check by using fractions. 9.5 / 19 in simplified form is 1/2, which is 1:2 in ratio.
It would be 9.5:19 just multiply 9.5 by 2
Matt is cutting quilt squares measuring 3 inches on each side he wants to use them to make a rectangular wall hanging measuring 1 yard by 2/1/2 feet how many quilt squares does he need
The answer is:
Matt will need 120 quilt squares.
Why?To solve the problem, we need to calculate the area of the wall and then, calculate how many quilt squares are needed.
We know that the wall measures 1 yard and 2 1/2 feet, also we know that the quilt squares measures 3 inches.
First, we need to conver the units:
So, converting we have that:
[tex]1yard=36inches[/tex]
Also,
[tex]1feet=12inches[/tex]
[tex]2.5*1feet=2.5*12inches[/tex]
[tex]2.5feet=30inches[/tex]
For the wall:
Calculating the area of the wall, we have:
[tex]Area_{rectangle}=base*height\\\\Area_{rectangle}=36inch*30inch=1080inch^{2}[/tex]
For the quilt squares:
Calculating the area of the quilt square, we have:
[tex]Area_{square}=side*side\\\\Area_{square}=3inch*3inch=9inch^{2}[/tex]
Therefore, to calculate how many quilt squares are needed, we need to use the following equation:
[tex]QuitSquaresNeeded=\frac{Area_{rectangle}}{Area_{square}}\\\\QuitSquaresNeeded=\frac{1080inch^{2}}{9inch^{2}}=120[/tex]
Hence, we have that Matt will need 120 quilt squares.
Have a nice day!
Answer:240
Step-by-step explanation:
i got this answer right on my school
Help please I don’t understand probability and need the correct answers to these questions.
Answer:
1) = 0.175
2) = 0.244
3) = 0.168
Step-by-step explanation:
Experimental, not theoretical, so we use the results table.
1. P(3 n Tails) = 62/(53 + 65 + 49 + 71 + 54 + 62) = 0.175
2. P(Woman n Up) = 39/(36 + 43 + 39 + 42) = 0.244
3. P(Tuna n Wheat Bread) = 23/(22 + 24 + 21 + 22 + 25 + 23) = 0.168
Which equation is represented by the table?
the answer is b=3a+2 so B
The answer is B hope this helped!
What is the value of X enter your answer in the box
Answer:
x = √(13² - 12²) = √(169 - 144) = √25 = 5
a model rocket is launched from a roof into a large field the path of the rocket can be modeled by the equation Y equals -0.05x^2 + 9.6 x + 5.4 where X is the horizontal distance in meters from the starting point on the roof and y is the height in meters of the rocket above the ground how far horizontally from its starting point will the rocket land round your answer to the nearest hundredth
•82.03 m
•6.50 m
• 90.00 m
• 88.53 m
The answer to this question is going to be 88.53 because you shift it horizontally
Answer:
it's 160 or 160. 56
Step-by-step explanation:
since you want the height horizontally from the starting height, and that height was 5.4 metres,
-.06x^2 + 9.6x + 5.4 = 5.4
the 5.4 drops out, so
x(-.06x + 9.6) = 0
x = 0 , the starting time
or
x = 9.6/.06 = 160
it will land after 160 m
A mailbox is in the shape of a prism. The area of the base is 52 square inches and the height is 18 inches. What is the volume of the mailbox
Answer:
The volume of the mailbox is [tex]936\ in^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the prism (mailbox) is equal to
[tex]V=Bh[/tex]
where
B is the area of the base of the prism
h is the height of the prism
we have
[tex]B=52\ in^{2}[/tex]
[tex]h=18\ in[/tex]
substitute
[tex]V=52(18)=936\ in^{3}[/tex]
Given that (-2,-1) is on the graph of f(x), find the corresponding point for the function f(x-4).
Answer:
(2, -1)
Step-by-step explanation:
The function f(x-4) represents a shift of f(x) 4 units to the right. Adding 4 to the x-coordinate of (-2, -1) puts it at (2, -1).
What’s the answer to this graph? Only if you really know please and thanks!!
Answer:
[tex]h(x)=5^x[/tex]
Step-by-step explanation:
All the graphs are growing bigger and bigger as x-values grows bigger.
This implies that the graphs represent exponential growth.
Hence their equation is in the form;
[tex]y=a^x[/tex]
The bigger the value of 'a' the faster the graph grows
We can see that h, grew faster than all the other graphs, hence 'a' should be the largest value, which is 5.
Therefore the function is :
[tex]h(x)=5^x[/tex]
Answer:
Correct choice is function [tex]h(x)=5^x[/tex]
Step-by-step explanation:
We have been given a graph of three functions f, g and h.
Now we need to find the best matching equation for the function h(x).
From graph we can see that all of the curves are increasing must faster as the move from left side to right side. That indicates they are exponential functions.
We know that if base is larger then graph will move upward much faster.
largest base from available bases is 5.
So the correct function is [tex]h(x)=5^x[/tex]
Volume of the cylinder is
of the volume of the cone.
Answer: The formula for the volume of a cylinder is v = πr2h. The volume for a cone whose radius is R and whose height is H is V = 1/3πR2H.
A point in the figure selected at random. find the probability that the point will be in the part that is NOT shaded.
Answer:
The probability that the point will be in the part that is NOT shaded is about 20% ⇒ 4th answer
Step-by-step explanation:
* Lets look to the figure
- There are four circles inscribed in a square
- The four circles touched each other and touched the four
sides of the square
∴ The side of the square = twice the diameter of a circle
- If the side of the square is l and the diameter of the circle is d
∴ l = 2d ⇒ divide the two sides by 2
∴ d = (1/2) l
∵ The radius of the circle = (1/2) the diameter
∴ r = (1/2) d
∵ d = (1/2) l
∴ r = (1/2)(1/2) l = (1/4) l
* Now lets find the area that NOT shaded
∵ The area of the square = side × side
∴ The area of the square = l × l = l²
∵ The area of the circle = πr²
∵ r = (1/4) l
∴ r² = [(1/4) l]² = (1/4)² × l² = (1/16) l²
∴ The area of one circle = (1/16)πl²
- The shaded part is the four circles
∴ The shaded area = 4 × (1/16)πl² = (1/4)πl²
- The part is not shaded = Area of the square - Area of the shaded part
∴ The area of not shaded = l² - (1/4)πl² ⇒ take l² as a common factor
∴ The area of not shaded = l²(1 -1/4 π)
- The probability that the point will be in the part that not shaded is
area of the part not shaded/area of the square
∴ P = l²(1 - 1/4 π)/l² ⇒ cancel l² from up and down
∴ P = (1 - 1/4 π )/1 = 0.2146 ≅ 0.2
- Chang it to percent number
∴ P = 0.2 × 100% = 20%
* The probability that the point will be in the part that is NOT shaded
is about 20%
∴ r = (1/2) d
∴
Please help me with this question in the picture
Answer:
I would say it's b because that makes the most sense tbh
Step-by-step explanation:
Answer:
every fifth student in seventh gradeStep-by-step explanation:
List possible outcomes
Answer:
2. A. H-red, H-blue, H-green, H-yellow, T-yellow, T-green, T-blue, T-red
3. 18
Step-by-step explanation:
2. Flipping a coin and spinning a 4-color spinner.
There are two possible outcomes for the coin: heads or tails (H or T).
There are still 4 possibilities for the spinner: red, blue, green and yellow
Since both are independent, you multiply the possible outcomes of each event, so 2 * 4 = 8 possible outcomes.
To list them all, take each possible outcome on one item (coin or spinner), and match it with all the possible outcomes of the other item.
So answer is A. H-red, H-blue, H-green, H-yellow, T-yellow, T-green, T-blue, T-red
3. Lunch combinations
You have 2 sandwiches, 3 sides and 3 beverages. How many different lunches can you make picking one of each?
As in the problem above, these possible outcomes are independent (choosing one specific sandwich has no impact on the side or the beverage).
So, to count all the possible outcomes, you just have to multiply the possible outcomes of each item, so
L = 2 sandwiches x 3 sides x 3 beverages = 18 possible lunches
Apex Precal please help
How many solutions are there for the system shown below?
2x^2+y^2=33
x^2+y^2+2y=19
A. 1
B. 4
C. 3
D. 2
Your answer for this question will be B.4
Answer:
Choice B; 4
Step-by-step explanation:
The solution to a system of equations is a pair of points (x, y) such that both equations pass through the given point. The number of solutions will thus be the number of such points where both functions pass through or intersect. The solutions to a system of equations can be determined analytically or graphically.
In this case, the graphical approach is much easier to use. We simply graph the two equations on the same graph and determine the number of points where they intersect.
From the attachment below, we see that the functions intersect at 4 distinct points. Hence there are 4 solutions to the system of equations given.