Answer:
The vertex form is f(x) = (x + 5)² + 12
The minimum value of f(x) is point (-5, 12)
Step-by-step explanation:
1) The vertex form of a quadratic equation f(x) = x² + 10·x + 37, which is the form f(x) = a·(x - h)² + k is found as follows;
For the general form of the quadratic equation, f(x) = a·x² + b·x + c
h = -b/(2·a) and k = f(h)
Therefore, for f(x) = x² + 10·x + 37,
a = 1, b = 10
∴ h = -10/2 = -5
k = f(-5) = (-5)² + 10×(-5) + 37 = 12
The vertex form is f(x) = a·(x - h)² + k gives;
f(x) = 1·(x - (-5))² + 12 = (x + 5)² + 12
The vertex form is f(x) = (x + 5)² + 12
2) The minimum value of x is found when d(f(x))/dx = 0
d(f(x))/dx = d(x² + 10·x + 37)/dx = 2·x + 10
d(f(x))/dx = 0 = 2·x + 10
x = -10/2 = -5
We check that it is the minimum by f''(x) being positive;
f''(x) = d(2·x + 10)/dx = 2 which is positive and x = -5 is the x-coordinate of the minimum value of f(x)
The x-coordinate of the minimum value of f(x) minimum value is f(-5) = (-5)² + 10×(-5) + 37 = 12
Therefore, we have;
The minimum value of f(x) = (-5, 12)
Answer:
The vertex is (-5,f(-5)=12), The minimum value of f(x) is 12.
CAN SOMEONE PLEASE HELP ME !!!!
Answer:
k = 29
29 + 6 = 35
-3 + 5 = 2
35 + 2 = 37
please help. pls show workings
Answer:
≈ 10.52 cm²
Step-by-step explanation:
The unshaded area is calculated as area of square subtract area of quarter circle, thus
A = 7² - [tex]\frac{1}{4}[/tex]πr²
= 49 - ( 0.25π × 7²)
= 49 - (0.25π × 49)
= 49 - 12.25π
≈ 10.52 cm² ( to 2 dec. places )
Answer:10.5cm^2
Step-by-step explanation:
Area of the square = L^2 =(7) ^2=49cm^2
Radius of quadrant = 7cm
Area of the quadrant =1/4 x πr^2
1/4 x 22/7 x (7) ^2
1/4 x 22/7 x 49
=38.5cm^2
Area of unshaded part= area of square - area of quadrant
49cm^2 - 38.5cm^2
=10.5cm ^2
Michael is trying to hang Christmas lights on his house. His house is 17 ft tall and the ladder leaning is 34 degrees above the ground. How long must the ladder be to reach the house? a 24 feet b 17 feet c 34 feet d 30 feet
Answer:
34 feet
Step-by-step explanation:
let length of ladder be x
[tex] \ \sin(34) = \frac{17}{x} [/tex]
[tex]x \sin(34) = 17[/tex]
[tex]x = \frac{17}{ \sin(34) } [/tex]
x = 32.131083564
a car traveling at 87 km/h and a bus leave a toll booth at the same time. twenty minutes later the bus is 3 km farther from the toll booth than the car. what is the average speed of the bus
Answer:
96 km/h
Step-by-step explanation:
Speed of car = 87 km/h
Time = 20 minutes = [tex]\frac{20}{60} = \frac{1}{3}\ hrs[/tex]
Distance traveled by bus = 3 km more than that of traveled by car
To find
Average speed of bus = ?
Solution:
Formula for distance traveled is given as:
[tex]Distance = Speed \times Time[/tex]
So, distance traveled by car in 20 minutes = 87 [tex]\times \frac{1}3[/tex] = 29 km
As per given statement, distance traveled by bus = 29 + 3 = 32 km
Time taken = [tex]\frac{1}{3}\ hrs[/tex]
Using the formula:
[tex]Speed = \dfrac{Distance}{Time}[/tex]
Speed of the bus =
[tex]\frac{32}{\frac{1}3} = \bold{96\ km/h}[/tex]
The projected worth (in millions of dollars) of a large company is modeled by the equation w = 236(1.06) t. The variable t represents the number of years since 2000. What is the projected annual percent of growth, and what should the company be worth in 2011? A. 6%; $448.00 million B. 16%; $474.88 million C. 16%; $250.16 million D. 6%; $422.64 million
Answer:
A. 6%, $448 million
Step-by-step explanation:
a) The base of the exponential term is 1.06, so the projected annual growth is 1.06 -1 = .06 = 6%
__
b) Filling in 11 for t, we find the projected worth to be ...
w = 236(1.06^11) ≈ $448 . . . million
What is x
I dont get it
Answer:
x = 35
Step-by-step explanation:
The angles of a triangle add to 180 degrees
103+ 42 + BCA = 180
BCA = 180 -103 -42
BCA =35
BCA and x are corresponding angles and corresponding angles are equal if the lines are parallel
7. The annual interest rate is 20%. The balance after the grace period was $15,000. A payment of $2,500 was made on the 3rd day. What is the interest for the month?
Answer:
Interest (I) = $18
Step-by-step explanation:
$15,000 by the end of grace period
$2,500 payment was made by the 3rd day
$15,000/$2500=6
6×3=18
I = PRT/100
I = (15,000 × 20% × 18 days)/100
I = {15,000 × 0.2 × (18/30)}/ 100
I= {15,000 × 0.2 × 0.6}/ 100}
I= {1800}/ 100}
I= {18}/ 1}
Interest (I) = $18
Square root & simplifying radicals
√30
Answer:
√30 =
5.4772255751
It can be simplified as this only, not more
it is 4km from Martina house to the nearest mailbox. how far is it in meters?
Answer:
4,000
Step-by-step explanation:
1 kilo = 1,000 meters.
find the slope of the line that contains (-1,2) and (2,2)
Answer:
[tex]slope=0[/tex]
Step-by-step explanation:
Use the slope formula:
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{rise}{run}[/tex]
Rise over run is the change in the y-axis over the change in the x-axis from one point to the other. This is also known as the "slope".
Insert the values:
[tex](-1_{x1},2_{y1})\\\\(2_{x2},2_{y2})\\\\\frac{2-2}{2-(-1)}\\\\\frac{2-2}{2+1}\\\\[/tex]
Simplify:
[tex]\frac{2-2}{2+1}=\frac{0}{3} =0[/tex]
The slope of the line is 0. This means that the two points lie on the same horizontal line.
:Done
Given the equation 4x−8y=32, a second equation that forms a system with no solution is: 1. x−2y=8 2. x−2y=32 3. x+2y=8 4. 2x−y=32
Answer:
2. x−2y=32.3
Step-by-step explanation:
Given 4x - 8y = 32, a second equation that forms a system with no solution is most easily found by reducing the given equation to x - 2y = 8; we can then easily compare this x - 2y = 8 to x - 2y = 32.3. These two lines are parallel and thus do not intercept, and thus the system has no solution.
The following frequency table shows the number of fish caught by each of Igor's family members. What was the maximum number of fish that a family member caught? _____ fish
Answer:
4
Step-by-step explanation:
The values on the left of the table represent the number of fish caught, and the number of the right of the table represents how many family members caught that amount of fish.
Therefore, the first row means that 0 family members caught 0 fish.
The second row means that 3 family members caught 1 fish.
The third row would mean 1 family member caught 2 fish.
The next row would mean 0 family members caught 3 fish.
And the final row would mean 4 family members caught 4 fish.
The question does not ask for the total amount of fish caught; rather is ask for the maximum number of fish that a single family member caught.
Therefore, the maximum amount of fish that a single family member catches is 4. (And 4 family members did so. But individually, the maximum amount of fish one person caught is 4).
Answer:
it's 1 fish
Step-by-step explanation:
i took the test
Y = 0.2(0.35)^t decay rate
Answer:
Step-by-step explanation:
At 1 year old it is: e1 = 2.7 mm high ... really tiny!
At 5 years it is: e5 = 148 mm high ... as high as a cup
At 10 years: e10 = 22 m high ... as tall as a building
At 15 years: e15 = 3.3 km high ... 10 times the height of the Eiffel Tower
At 20 years: e20 = 485 km high ... up into space!
Compute the value of each expression: |−12|−2|−6|
Answer:
12, 2, 6
Step-by-step explanation:
2
3
4
5
Which expression is equivalent to (f + g)(4)?
f(4) + g(4)
f(x) + g(4)
f(4 +
| + g(4))
4(f(x) + g(x))
Answer:
(f + g)(4) = f(4) + g(4)
Step-by-step explanation:
(f + g)(4) = f(4) + g(4)
___
The notation (f+g)(x) means that the value of f(x) is added to the value of g(x).
Solve for x. PLZ ANSWER FAST
Answer:
No solutions.
Step-by-step explanation:
7(2) + 39 > 53 and 16(2) + 15 > 31
14 + 39 > 53 and 32 + 15 > 31
53 >_ 53 but, 47 > 31 :/
So even with one the first equation is smaller.
PLEASE ANSWER QUICKLY ASAP
READ THE QUESTION CAREFULLY PLEASE
Answer:
140°
Step-by-step explanation:
total angle of a hexagon is 720. We know already 510°. That leaves 210°. The ratio between the two angles is 2:1, therefore angle CDE is 140° and angle DEF is 70 °
Answer:
140°
Step-by-step explanation:
We know that all of these angles here are part of a hexagon, meaning that their angle measures will all add up to 720°.
We can use what we already know and find what CDE and DEF will add up to.
[tex]145+90+160+115=510\\720-510=210[/tex]
Now, assuming x is the measure of DEF, we can create an equation for this.
[tex]x + 2x = 210\\3x = 210\\x = 70[/tex]
This is the measure of DEF, but it asks for CDE, which is twice the size of DEF. So
[tex]70\cdot2=140[/tex]
We can double check this is right by adding up all the measures.
[tex]145+90+160+115+140+70=720[/tex]
Hope this helped!
67.77759 rounded to nearest meter
Answer:
68
Step-by-step explanation:
0.7 rounds to 1 so add 1 to 67 to get 68
NEED HELP!
Create a table of points from the equation f (x)= 3x^2 -8x + 2
Answer:
The second table
Step-by-step explanation:
To create table of points using the function, [tex] f(x) = 3x^2 - 8x + 2 [/tex], substitute the value of x in each case.
Thus,
For x = -1,
[tex] f(-1) = 3(-1)^2 - 8(-1) + 2 = 3(1) + 8 + 2 = 3 + 8 + 2 [/tex]
[tex] f(-1) = 13 [/tex]
For x = 0
[tex] f(0) = 3(0)^2 - 8(0) + 2 = 3(0) - 0 + 2 = 0 - 0 + 2 [/tex]
[tex] f(0) = 2 [/tex]
For x = 1,
[tex] f(1) = 3(1)^2 - 8(1) + 2 = 3(1) - 8 + 2 = 3 - 8 + 2 [/tex]
[tex] f(1) = -3 [/tex]
For x = 2,
[tex] f(2) = 3(2)^2 - 8(2) + 2 = 3(4) - 16 + 2 = 12 - 16 + 2 [/tex]
[tex] f(2) = -2 [/tex]
For x = 3,
[tex] f(3) = 3(3)^2 - 8(3) + 2 = 3(9) - 24 + 2 = 27 - 24 + 2 [/tex]
[tex] f(3) = 5 [/tex]
The second table is the correct answer.
the length of a basketball pitch can be divided into 12 parts which 25 centimetres on how much parts it's 20 centimetres long can be obtained from the pitch
Answer:
the number of parts is going to be
= 15 parts
Step-by-step explanation:
A basketball pitch can be divided into twelve(12) parts , each part of equal length of twenty five (25) centimeters.
The initial and total length of the basketball pitch = 12*25
The initial and total length of the basketball pitch = 12*25
The initial and total length of the basketball pitch = 300 cm
So if it's now divided into parts of each 20 cm ,
the number of parts is going to be
= 300/20
the number of parts is going to be
= 15 parts
A ship drops its anchor into the water and creates a circular ripple. The radius of the ripple increases at
a rate of 50 cm/s. If the origin is used as the location where the anchor was dropped into the water.
Find the equation for the circle 12 seconds after the anchor is dropped
Please write all the steps it’s for my summer school test and I need it done quick as possible thanks.
Answer:
The equation for the circle 12 seconds after the anchor is dropped is x^2 + y^2 = 360,000
Step-by-step explanation:
To find the equation for the circle 12 seconds when the radius of the ripple increases at a rate of 50 cm/s, the circle radius will be;
50 * 12 = 600 cm
Then place the equation inform of Pythagoras equation which is;
x^2 + y^2 = r^2
Where r is the radius
x^2 + y^2 = 600^2
x^2 + y^2 = 360,000
Then, the equation for the circle 12 seconds after the anchor is dropped is x^2 + y^2 = 360,000
Find the missing probability: P(B)=7/20, P(A|B)=1/4, P(A∩B)=?
Answer:
P(A∩B) = 7/80
P(A∩B) = 0.0875
Step-by-step explanation:
Given
P(B)=7/20
P(A|B)=¼
Required
P(A∩B)=?
The given probability shows conditional probability and the relationship between the given parameters is as follows.
P(A∩B) = P(B) * P(A|B)
Substitute ¼ for P(A|B) and 7/20 for P(B)
The expression
P(A∩B) = P(B) * P(A|B) becomes
P(A∩B) = 7/20 * ¼
P(A∩B) = 7/80
P(A∩B) = 0.0875
Hence, the calculated P(A∩B) is 7/80 or 0.0875
Complete the statements. f(4) is . f(x) = 4 when x is
Answer:
x=4
Step-by-step explanation:
it's a identity function because it is in the form of f(x)= x ,so the value of x is 4.
Which expression is not equivalent to the other expressions?
-6(2x-4)
-(12x-6)+18
-3(4x-3)+15
-4(3x+6)
The map of a biking trail is drawn on a coordinate grid. The trail starts at P(−2, 1) and goes to Q(6, 1). It goes from Q to R(6, −3) and then to S(9, −3). What is the total length (in units) of the biking trail? 11 15 18 19
Answer:
19
Step-by-step explanation:
Answer:
Hey there!
We use the distance formula to find the distances between each of these points.
From -2, 1 to 6, 1 is a total of 8 units.
From 6, 1 to 6, -3 is a total of 4 units.
From 6, -3 to 9, -3 is a total of 3 units.
8+4+3=15 units.
Let me know if this helps :)
At an elite baseball camp, 60% of players can bat both right-handed and left-handed. If 25% of the players who bat left-handed do not bat right-handed, what is the probability that a player selected at random does not bat left-handed?
Answer:
The probability that a player selected at random does not bat left-handed is 20%.
Step-by-step explanation:
Assume that there are a total of 100 baseball players at an elite baseball camp.
The information provided is:
60% of players can bat both right-handed and left-handed. 25% of the players who bat left-handed do not bat right-handed.That is, the number of players can bat both right-handed and left-handed is,
n (L and R) = 60.
Now, if 25% of the players who bat left-handed do not bat right-handed, then 75% of all left-handed players can also bat right-handed.
⇒ n (L and R) = n (L) × 75%
60 = n (L) × 0.75
n (L) = 60/0.75
n (L) = 80
So there are 80 left handed batters.
Compute the number of only left handed batters as follows:
n (Only L) = n (L) × 25%
= 80 × 0.25
= 20
So there are 20 only left handed batters.
Compute the number of only right handed batters as follows:
Total = n (Only L) + n (Only R) + n (L and R)
100 = 20 + n (Only R) + 60
n (Only R) = 20
Thus, the probability that a player selected at random does not bat left-handed is 20%.
Find the value of x in the given
right triangle.
Enter your answer as a decimal rounded to the
nearest tenth.
Answer:
x = 12.5Step-by-step explanation:
Since the figure above is a right angled triangle we can use trigonometric ratios to find x
To find x we use cosine
cos∅ = adjacent / hypotenuse
From the question
The hypotenuse is x
The adjacent is 10
Substitute these values into the above formula and solve for x
That's
[tex] \cos(37) = \frac{10}{x} [/tex][tex]x \cos(37) = 10[/tex]Divide both sides by cos 37
[tex]x = \frac{10}{ \cos(37) } [/tex]x = 12.52135
We have the final answer as
x = 12.5 to the nearest tenthHope this helps you
Answer:
probably 16.5
Step-by-step explanation:
Please solve.
Essie likes plants. She never misses a chance to go to the nursery section in Home Depot. Essie has a total of $65.50 to spend on her trips to the store over the next three days. On her second trip to the nursery she spent $15.50 dollars more than what she spent on the first trip to the store. On her third trip to the nursery she spent two times much as what she spent on her first trip to the nursery. How much did she spend on her first trip to the nursery? Create a linear equation to model a real-world situation and solve the equation to find the solution
Answer:
Step-by-step explanation:
Let $ x = the amount spent on the first day
The amount spent on the second day = x + 15.50
The amount spent on the third say = 2*x = 2x
Total amount Essie spent on 3 days = $65.50
x + (x +15.50) + 2x = 65.50
x + x + 15.50 + 2x = 65.50
Add like terms
4x + 15.50 = 65.50
Subtract 15.50 from both sides
4x = 65.50 - 15.50
4x = 50
Divide both sides by 4
x = 50/4
x = $ 12.50
The amount spent on the first day = $ 12.50
The amount spent on the second day = 12.50 + 15.50 = $ 28
The amount spent on the third day= 12.50 * 2 = $ 25
I am an odd two-digit number. The sum of my two digits is 10 and the difference of my two digits is 0. What number am I?
In a test (+5) marks are given for every correct answer and (-2) marks are given for every incorrect answer. Radhika answered all the questions and scored 30 marks though she got 10 correct answers. How many incorrect answers had they attempted?
Answer:
10 incorrect answers
Step-by-step explanation:
From the information given, you can say that 5 marks for the number of correct answers minus two marks for the number of incorrect answers is equal to 30 that is the score that Radhika got:
(5*10)-2x= 30, where x is the number of incorrect answers.
Now, you can solve for x:
50-2x=30
50-30=2x
20=2x
x=20/2
x=10
According to this, the answer is that they attempted 10 incorrect answers.
