I have a question that has already been answered. I just need someone to please explain the steps.
Find the coordinates of the minimum point of the function- f(x) = x^2 + 4x - 5.
Solution-
We need to express x^2 + 4 - 5 in the form (x+h)^2 + k.
Let x^2 - 4x = (x - 2)^2 - 4 (Where did the -4 come from?)
x^2 + 4x - 5 = [ (x - 2)^2 - 4] - 5
= (x - 2)^2 - 9
All I wanna know is where the -4 came from. what rule must be applied.
Answer:
Step-by-step explanation:
Using brackets will really help.
y = (x^2 + 4x + ... ) - 5 You are trying to complete the square. The square in this case is a trinomial that is squared.
To do that, you take 1/2 the linear term (4x)/2, drop the x (4/2), and square the result (4/2)^2. The number is 2^2 which is 4.
So far what you have is
y = (x^2 + 4x + 4) - 5
Now you just can't add 4 without adjusting it somehow. If you do, the whole question will change it's value. Because you added 4 inside the brackets, you must subtract 4 outside the brackets.
What that means is 4 inside - 4 outside. So it looks like this
y = (x^2 + 4x + 4) - 5 - 4
Now you continue on
y = (x + 2)^2 - 9 The 4 combines with the 5 to make nine.
In the diagram below, what is the measure of angle 1?
Answer: 82 degrees
Step-by-step explanation:
Why to solve this question
Answer:
35°, 70°, 75°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180° , then
x + 2x + 75 = 180
3x + 75 = 180 ( subtract 75 from both sides )
3x = 105 ( divide both sides by 3 )
x = 35
2x = 2 × 35 = 70°
The angles in the Δ are 35°, 70°, 75°
The three angles of the triangle are 75°, 70° and 35°.
Step-by-step explanation:
We know that,
Sum of angles of a triangle = 180°
⇢ 75° + 2 x + x = 180°
⇢ 3x = 180° - 75°
⇢ 3x = 105°
⇢ x = [tex] \frac{105}{3} [/tex]
⇢ x = 35°
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A jar contains 2 orange, 4 green, 2 white and 2 black balls. What is the probability of drawing an orange ball without putting it back, then drawing a black ball? (write your answer as a simplified fraction)
Answer:
2/45
Step-by-step explanation:
We are told that:
A jar contains 2 orange, 4 green, 2 white and 2 black balls.
The total number of balls in the jar is calculated as:
2 orange balls + 4 green balls + 2 white balls + 2 black balls = 10 balls
The probability of drawing an orange ball = P(Orange) = 2/10
The probability of drawing a black ball = P(Black) = 2/10
Therefore, the probability of drawing an orange ball without putting it back, then drawing a black ball is calculated as:
2/10 × 2/9 = 4/90
= 2/45
Decide if the following statement is valid or
invalid.
If you live in Miami, then you live in Florida.
Jada lives in Florida, so she lives in Miami.
Valid
Invalid
Answer:
Invalid
Step-by-step explanation:
Answer:
Invalid
Step-by-step explanation:
You can live in Florida outside of Miami.
FBISD bought 12 new chairs for $28.99 each, and 8 tables for $45.50 each. What is the total price, including 8.25% sales tax.
A)$772.39
B)$711.88
C)$347.88
D)$60.51
Please hurryyyyy please
Answer:
d
Step-by-step explanation:
Carly buys 3 more band concert tickets than choir concert tickets. Band concert tickets cost $3.50 per ticket. What is the cost for the choir concert and band concert tickets?
Answer:
I'm not to sure, but I'll say 10.5
If you multiply 3.50 x 3 you'll get 10.5
If you add you'll get 13.5.
If it's an addition I'll recommend to go with 13.5
If it's a multiplication I'll recommend to go with 10.5
A spherical boulder is 12 ft in diameter and weighs almost 8 tons. Find the volume. Use 3.14 for pi.
Answer:
904.32 ft^3
Step-by-step explanation:
Volume of a sphere = 4/3 x pi x r^3
r = 12/2 = 6
the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.
A radius is half of the diameter
4/3 x 3.14 x 6^3 = 904.32 ft^3
"The product of four and a
number is more than ten."
Answer:
x>5/2
Step-by-step explanation:
4x>10
x>10/4
x>5/2
the perimeter of a rectangle parking lot is 322 m. if the length of the parking lot is 86 m, what is the width
156 divided by 3 with remaining
Answer: 52
Step-by-step explanation:
Divide 156 by 3, you get 52 with a remainder of 0.
In long division, you would write it as:
To perform the division, start by dividing 3 into the first digit of 156, which is 1.
3 ) 156 ( 52
- 15
_______
6
-6
_______
0
3 cannot go into 1, so you move to the next digit, 15. 3 can go into 15 five times (3 * 5 = 15). After subtracting 15 from 15, you have 0.
Now, you bring down the last digit, 6, to form 6. Since 3 can go into 6 two times (3 * 2 = 6), the final quotient is 52, and the remainder is 0.
In summary, 156 divided by 3 is equal to 52, with no remaining or fractional parts.
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PLS HELP!! GIVING BRAINLIEST!! :((
Ian Uses The Rule Add 1/2 Then Multiply By 2 Starting From 0
Answer:
1 3 7 15 31
Step-by-step explanation:
i used a calculator. Calculator Soup® is a good website for calculating stuff
pls help me with this
Answer:
D at 8.8
im not sure brainliest please ok
Answer:
The answer is C at 8.1.
Step-by-step explanation:
To find [tex]\sqrt{66}[/tex], start by finding the two consecutive perfect squares that 66 lies between them. The two perfect squares are 64 ([tex]8^{2}[/tex]) and 81 ([tex]9^{2}[/tex]). So, the whole number part of the square root of 66 will be 8.
Now, for the decimal part, use the following formula:
(Given number - Smaller perfect square) / (Greater perfect square - Smaller perfect square)
Then, put in the known information, which will look like:
(66 - 64)/(81 - 64) = 2/17 = 0.117
Finally, [tex]\sqrt{66}[/tex] is 8.117, so the answer is C at 8.1.
Write an exponential function in the form y=ab^x that goes through points (0,12) and (3,6144)
Given:
An exponential function goes through points (0,12) and (3,6144).
To find:
The exponential function.
Solution:
The general exponential function is:
[tex]y=ab^x[/tex] ...(i)
The function goes through point (0,12). Substituting [tex]x=0,y=12[/tex], we get
[tex]12=ab^0[/tex]
[tex]12=a[/tex]
The function goes through point (3,6144). Substituting [tex]a=12, x=3,y=6144[/tex] in the general exponential function, we get
[tex]6144=12b^3[/tex]
[tex]\dfrac{6144}{12}=b^3[/tex]
[tex]512=b^3[/tex]
[tex]512^{\frac{1}{3}}=b[/tex]
[tex]8=b[/tex]
Putting [tex]a=12,b=8[/tex] in (i), we get
[tex]y=12(8)^x[/tex]
Therefore, the required exponential function is [tex]y=12(8)^x[/tex].
Question 7 of 10
These box plots show daily low temperatures for a sample of days in two
different towns.
Degrees (F)
Which statement is the most appropriate comparison of the spreads?
Answer:
A
Step-by-step explanation:
In a box plot, interquartile range (IQR) can be used to describe the spread of any given data.
IQR = Q3 - Q1
✔️IQR for Town A:
Q3 = 40
Q1 = 20
IQR = 40 - 20 = 20°
✔️IQR for Town B:
Q3 = 30
Q1 = 20
IQR = 30 - 20 = 10°
We can conclude that the IQR for town A, 20°, is greater than the IQR for town B, 10°.
42÷(13×6×7)=
I need help
Answer:
The answer is 1/13
Step-by-step explanation:
42÷(13×6×7)
= 42÷546
= 1/13
Your living room is carpeted but you have allergies, and need to cover the 9 points floor with hardwood panel flooring. The panel flooring at Lowes cost $3.19 per square foot. (scale: 1m = 3.28 ft) Hint: Each unit contains 32.29 square feet. How much will it cost to purchase the flooring panels? (round to the nearest cent)
HELPPPPPPPP
Answer:
$103
Step-by-step explanation:
Your living room is carpeted but you have allergies, and need to cover the 9 points floor with hardwood panel flooring. The panel flooring at Lowes cost $3.19 per square foot. (scale: 1m = 3.28 ft) Hint: Each unit contains 32.29 square feet. How much will it cost to purchase the flooring panels? (round to the nearest cent)
From the above question:
1 square foot = $3.19
32.29 square feet = x
Cross Mulitiply
x = 32.29 × $3.19
x = $103.0051
Approximately to the nearest cent = $103
Therefore, it will cost $103 to purchase the flooring panels
What is the focus of the parabola?
y =1/4x^2 -x-1
Enter your answer in the boxes.
Answer:(-y/(1/2)) -x/(1/2)=1
Step-by-step explanation:
The coordinates of the focus of the parabola are (2, -1.9375)
How to determine the focus?The equation of the parabola is given as:
[tex]y = \frac 14x^2 - x - 1[/tex]
Express as a vertex form
[tex]y = \frac 14(x - 2)^2 - 2[/tex]
The focus of a quadratic function of the form [tex]y = a(x - h)^2 + k[/tex] is
Focus = (h, k + 1/4 a)
By comparing [tex]y = a(x - h)^2 + k[/tex] and [tex]y = \frac 14(x - 2)^2 - 2[/tex], we have:
a = 1/4
h = 2
k = -2
So, we have:
Focus = (2, -2 + 1/4 * 1/4)
Evaluate
Focus = (2, -1.9375)
Hence, the coordinates of the focus of the parabola are (2, -1.9375)
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Bob's gift shop sold a record number of cards for Mother's Day. One salesman sold 24
cards, which was 20% of the cards sold for Mother's Day. How many cards were sold
for Mother's Day?
Answer:
120
Step-by-step explanation:
20 * 5 = 100 so we multiply 24 by 5 and that equals 120
f(x) = x2
g(x) = 3x2
Which option could show the graphs of f and g?
Answer:
2 Transformations
Step-by-step explanation:
A reflection in the x axis accounts for the minus sign and because there's a 3 there, it is a stretch in the y direction scale factor 3. hope this helps :)
Which graph shows the line that best fits the data points given?
Answer:
3rd one
Step-by-step explanation:
The correct graph which shows the line that best fits the data points given is shown in Option 3.
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
To find correct graph which shows the line that best fits the data points.
Now, We know that;
The correct graph of line for the data points is contain almost every points.
Hence, We get;
The correct graph which shows the line that best fits the data points given is shown in Option 3.
Thus, The correct graph which shows the line that best fits the data points given is shown in Option 3.
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Bob walks 8/10 of a kilometer to school each day. How many kilometers does bob walk to school in 5 days ?
Answer:
4 in 5 days
Step-by-step explanation:
What’s the answer to this question 6 1/2 - 4 7/10
Answer:
1 4/5
Step-by-step explanation:
Convert 1/2 to tenths. 1/2 = 5/10 which reduces back to 1/2
borrow 1 from the 6 to make 5/10 greater than 7/10
5/10 + 10/10 = 15/10
The 6 1/2 has become 5 and 15/10
5 15/10 Subtract 4 7/10
4 7/10
1 8/10 Reduce the fraction by dividing top and bottom by 2
1 4/5
Also possible is
6.5
4.7 Subtract
1.8
There are 8 blue marbles, 3 red marbles, and 4 yellow marbles in a bag. What is the probability of selecting a purple marble on the first draw?
Answer:
0
Step-by-step explanation:
there is only blue marbles, yellow marbles, and red marbles. there are no purple marbles so you’d be unable to pull out a purple one no matter how many times you tried. so the probability would be 0
1000 + 874 + 53528 - 1026 =
Answer:
54376
is the answer .......
what is the value of x
Answer:
8
Step-by-step explanation:
Lines have angles that are equal to 180. Therefore, because we already have 140 of the 180 necessary, we can subtract 140 from 180 to get 40. 40 divided by 5 is 8.
Hope that this helps!
Answer:
I. x=8
Step-by-step explanation:
lines form 180° angles so
140 +5x= 180 ; subtract 140 from both sides
5x= 180-140; divide both sides by 5
x= 40/5 = 8
Help please?!?!??!?!!!?!?!?!?!?!?!?!!?!?!?
Answer:
16.7%
Step-by-step explanation:
Probability is defined by the formula: the number of desirable outcomes over the total outcomes. The total number of outcomes is the sum of all shoes that he could possibly pick:
5 + 7 + 1 + 4 + 6 + 8 + 2 + 3 = 36
And the desirable outcomes are those where he picks brown boots, which is 6 outcomes.
Using the formula for probability, we get the expression: 6/36 to represent the probability. It simplifies to 1/6 which is about 16.7%
Solve 22 = - 3d + 1. Show your steps.
Answer and Step-by-step explanation:
Solve for D.
Subtract 1 from both sides of the equation.
22 - 1 = -3d + 1 - 1
21 = -3d
Divide both sides by -3.
21 ÷ -3 = -3d ÷ -3
-7 = d
d is equal to -7.
#teamtrees #PAW (Plant And Water)
What is the product of 4 cos
14 (cos(37) + i sin (34) and 2 (cos(5) + sin(5)}?
--4 cot (--45)
cos (390)
sin (330)
Fill in the table using this function rule. y=6x + 5
Answer:
11, 17, 29, 65
Step-by-step explanation:
Rrplace x with values on the x colon
Answer:
Column 1 (When x = 1): y = 11
Colum 2(When x = 2): y = 17
Column 3(When x = 4): y = 29
Colum 4(When x= 10): y = 65
Step-by-step explanation:
When x = 1; y = 6(1) + 5
=> y = 6 + 5
=> y = 11
When x = 2; y = 6(2) + 5
=> y = 12 + 5
=> y = 17
When x = 4; y = 6(4) + 5
=> y = 24 + 5
=> y = 29
When x = 10; y = 6(10) + 5
=> y = 60 + 5
=> y = 65
Hope this helps!