Final answer:
To complete the square for f(x) = x^2 - 6x + 19, we create a perfect square trinomial to rewrite the function as f(x) = (x - 3)^2 + 10, which has a minimum value at the vertex (3, 10).
Explanation:
To complete the square for the quadratic function f(x) = x2 - 6x + 19, we need to form a perfect square trinomial from the x2 and the -6x terms and then adjust the constant term accordingly.
First, we divide the coefficient of the x term, which is -6, by 2, getting -3, and then square it to get 9. We add and subtract this number inside the function to maintain the equality:
f(x) = (x2 - 6x + 9) - 9 + 19
Now, f(x) becomes:
f(x) = (x - 3)2 + 10
Since the coefficient of the x2 term is positive, the parabola opens upward, and the vertex represents the minimum value of the function.
The vertex of the parabola is at (3, 10), so f(3) = 10 is the minimum value of f(x). Therefore, the correct answer is:
D) f(x) = (x - 3)2 + 10 and f(x) has a minimum value f(3) = 10.
Is 6 15/28 or 6 5/9 bigger?
Answer:
[tex]6 \frac{5}{9} [/tex]
is greater than
[tex]6 \frac{15}{28} [/tex]
Answer:6 5/9 is greater than 6 15/28
Step-by-step explanation: positive proper fractions: 15/28, 5/9;
1 positive integer number: 6; Any positive proper fraction is smaller than
any positive integer number Sort the positive proper fractions:
15/28 and 5/9 15/28 already reduced to the lowest terms;
the numerator and the denominator have no common prime factors:
15 = 3 × 5;
28 = 22 × 7;
5/9 already reduced to the lowest terms;
the numerator and the denominator have no common prime factors:
5 is a prime number;
9 = 32; 15 = 3 × 5;
5 is a prime number;
Multiply all the unique prime factors, by the largest exponents:
LCM (15, 5) = 3 × 5 = 15 Divide LCM by the numerator of each fraction:
For fraction: 15/28 is 15 ÷ 15 = (3 × 5) ÷ (3 × 5) = 1;
For fraction: 5/9 is 15 ÷ 5 = (3 × 5) ÷ 5 = 3; Build up all the fractions to the same numerator (which is LCM).
Multiply the numerators and the denominators by their expanding number:
15/28 = (1 × 15)/(1 × 28) = 15/28;
5/9 = (3 × 5)/(3 × 9) = 15/27;
Can anyone solve the 8th question given below??? Urgent!!
Answer:
AY = 10 cm.
Step-by-step explanation:
Given that, ΔABC is similar to ΔAXY
and [tex]\frac{AB}{AX } = \frac{5}{3}[/tex]
⇒ [tex]\frac{AC}{AY } = [tex]\frac{BC}{XY } = \frac{5}{3}[/tex]
⇒ BC = XY× \frac{5}{3}[/tex] = \frac{20}{3}[/tex] (as XY = 4 cm given)
Now, check the attached figure,
given, BY bisects ∠XYC
let ∠XYB = ∠BYC = x
⇒ ∠AYX = 180-2x (angle on a straight line)
and also ∠AYX = ACB (similar triangle properties)
⇒ ∠ACB = 180-2x
Now, sum of angles in ΔBYC = 180°
⇒ ∠YBC = x
⇒ BC = YC (as two sides of equal angles are equal in a triangle)
⇒ YC = \frac{20}{3}[/tex]
And also [tex]\frac{AC}{AY } = \frac{5}{3}[/tex]
AC = AY + YC
⇒ [tex]\frac{AY+YC}{AY } = \frac{5}{3}[/tex]
⇒ [tex]\frac{AY+\frac{20}{3}[/tex]}{AY } = \frac{5}{3}[/tex]
⇒ 5AY = 3AY + 20
⇒ AY = 10 cm
In which of the following functions would it be appropiate to use only positve integers for the domain?Select all that apply.
Complete Question:
As you may have unintentionally forgotten to add the answer choices in your question, but I was able to find the complete the question and answering your question based on this as it may surely clear your concepts. Here is the complete question.
In which of the following functions would it be appropriate to use only positive integers for the domain? Select all that apply.
The function c(p) represents The cost for P people to attend the movies. The function m(t) represents the miles driven over T hours. The function t(m) represents the average high temperature for a given number of months. The function p(w) represents the prophet of a farmer who sells whole watermelons. The function h(n) represents the number of person-hours it takes to assemble n engines in a factory.
Answer Explanation:
Domain is termed as all the input values on a certain interval that define the function.
Here are the appropriate function scenarios where it is appropriate to use only positive integers.
The function c(p) represents The cost for P people to attend the movies.
As the function c(p) contains people. And People are not counted as negative, although they can be zero. So, only positive integers should be appropriate to use in this scenario.
The function m(t) represents the miles driven over T hours
As the function m(t) contains miles. And miles are not counted as negative. They normally initiate with 1. So, only positive integers should be appropriate to use in this scenario.
The function t(m) represents the average high temperature for a given number of months.
As the function t(m) contains months. And months are not counted as negative. They normally initiate with 1. So, only positive integers should be appropriate to use in this scenario.
The function p(w) represents the prophet of a farmer who sells whole watermelons.
As the function p(w) contains the number of watermelons. And watermelons are not counted as negative. They normally initiate with 1. So, only positive integers should be appropriate to use in this scenario.
The function h(n) represents the number of person-hours it takes to assemble n engines in a factory.
As the function h(n) contains the number of engines. And engines are not counted as negative. They normally initiate with 1. So, only positive integers should be appropriate to use in this scenario.
Keywords: domain, function, positive integer
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can you help find the quotient for 4/5 ÷ 10
Answer:
2/25
Step-by-step explanation:
Answer:
0.08
Step-by-step explanation:
If (3, 5) is a solution of both y= 4x + 7 and y=5, what is the solution of 4x + 7=5?
Answer:
Step-by-step explanation:
X=-1/2
Hope this helps mark me as brainiest pls
Yes, -1/2 will be the x-coordinate for the solution. We can also find the y-coordinate by subbing in -1/2 for x in the equation y=4x+7.
y=4(-1/2)+7
y=-2+7
y=5
The intersection point would be (-1/2,5).
What is 6 to the power of “h” equal to 126
Answer:
6^h=126
Step-by-step explanation:
6 to the power of h is just 6^h
Plug it into an equation with =126
Boom you have the equation 6^h=126
Simplify -12x^4/x^4+8x^5
Answer:
OPTION A: [tex]$ \frac{12}{1 + 8x} $[/tex], where [tex]$ x \ne - \frac{1}{8} $[/tex].
Step-by-step explanation:
Given: [tex]$ \frac{- 12x^4}{x^4 + 8x^5} $[/tex]
Taking [tex]$ x^4 $[/tex] common outside in the denominator, we get:
[tex]$ = \frac{-12x^4}{(x^4)(1 + 8x)} $[/tex]
[tex]$ x^4 $[/tex] will get cancelled on the numerator and denominator, we get:
[tex]$ = \frac{-12}{1 + 8x} $[/tex]
we know that the denominator can not be zero.
That means, 1 + 8x [tex]$ \ne $[/tex] 0.
[tex]$ \implies 8x \ne -1 $[/tex]
[tex]$ \implies x \ne \frac{-1}{8} $[/tex]
So, the answer is: [tex]$ \frac{-12}{1 + 8x} $[/tex], where [tex]$ x \ne \frac{-1}{8} $[/tex].
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Find the area. You answer will be a decimal.
_________ ft²
Answer:
26.4 ft^2 (1 d.p.)
Step-by-step explanation:
[tex]area \: of \: circle = \pi {r}^{2} [/tex]
Since it is given that r, the radius of the circle, is 2.9 ft,
area of circle= π(2.9)^2= 8.41π= 26.4 ft^2 (1 d.p.)
A triangle has an area of 52 square meters. and a height of 13 meters. Find the length of the base.
Answer:
Length of the base = 8
Step-by-step explanation:
Area of a triangle = 1/2(h*b)
h = height
b = base
52 = 1/2 (13 * b)
Rearrange the equation to get b on it's own
52 * 2 = 13 * b
104 = 13 * b
104/13 = b
b = 8
A = 1/2(bh)
in this case, b = 2a/h. plug in the values:
steps
b = 2a/h
b = 2(52)/13
b = 104/13
b = 8 meters
At 8am Sunday morning, the temperature was 35 degrees Fahrenheit. A student recorded the change in temperature at 8:00am for the next three days. Which number line shows a point representing the temperature on Wednesday morning at 8:00am? *
Answer:
B. 28 degrees
Step-by-step explanation:
ok so,
the starting temperature is 35 degrees then the temperature dropped 4 degrees. making the temp 31 degrees. next the temperature rose 2 degrees, making it 33 degrees. lastly, the temperature dropped another 5 degrees making it 28 degrees out on wednesday.
so the number line showing this would be B.
Final answer:
After a cold front caused the temperature to drop by 40 degrees from the initial 35 degrees Fahrenheit, the resulting temperature would be -5 degrees Fahrenheit on the number line for Wednesday morning at 8:00am.
Explanation:
The student originally observed a temperature of 35 degrees Fahrenheit on Sunday morning. If we suppose a cold front blows in and drops the temperature by 40.0 Fahrenheit degrees, the temperature change can be calculated by subtracting 40 from the initial temperature:
35 °F - 40 °F = -5 °F
Therefore, the number line that shows the temperature on Wednesday morning at 8:00am should have a point at -5 degrees Fahrenheit, representing the new temperature after the cold front.
Input value of which f (x)=3
Answer:
y = 3
Step-by-step explanation:
A.
discrete
B.
continuous
C.
linear
D.
nonlinear
E.
increasing
F.
decreasing
G.
both increasing and decreasing
H.
neither increasing nor decreasing
B Jamal says that 18:12 and 3:4 are not equivalent ratios Margie says they are equivalent ratios who is correct
Answer:
Jamal is correct.
Step-by-step explanation:
3:4 is equivalent to 9:12, not 18:12.
We can see that for 3:4, the left side is less than the right, but for 18:12, left side is greater than the right, which immediately tells us the ratios are not equivalent.
Jamal is correct. 18:12 and 3:4 are not equivalent ratios.
Equivalent ratiosTo determine if two ratios are equivalent, you can simplify them to their simplest form or find a common factor that divides both terms. In this case:
18:12 can be simplified by dividing both terms by their greatest common factor, which is 6:
18 ÷ 6 = 3
12 ÷ 6 = 2
So, 18:12 simplifies to 3:2.
Now, compare it to 3:4. Since they have different values (3:2 vs. 3:4), Jamal's statement is incorrect, and Margie is right; they are not equivalent ratios.
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write an equation for the line that passes through the given point and is parallel to the graph of the given equation.
(10, -5) y= 3/2x-7
(6,2) y= 2/3x+19
Answer:
[tex]\displaystyle 2x - 3y = 6\:OR\:y = \frac{2}{3}x - 2 \\ \\ 3x - 2y = 40\:OR\:y = \frac{3}{2}x - 20[/tex]
Step-by-step explanation:
2 = ⅔[6] + b
4
[tex]\displaystyle -2 = b \\ \\ y = \frac{2}{3}x - 2[/tex]
If you want it in Standard Form:
y = ⅔x - 2
- ⅔x - ⅔x
_________
−⅔x + y = −2 [We do not want fractions in our standard equation, so multiply by the denominator to get rid it.]
−3[−⅔x + y = −2]
[tex]\displaystyle 2x - 3y = 6[/tex]
_______________________________________________
−5 = 3⁄2[10] + b
15
[tex]\displaystyle -20 = b \\ \\ y = \frac{3}{2}x - 20[/tex]
If you want it in Standard Form:
y = 3⁄2x - 20
- 3⁄2x - 3⁄2x
__________
−3⁄2x + y = −20 [We do not want fractions in our standard equation, so multiply by the denominator to get rid of it.]
−2[−3⁄2x + y = −20]
[tex]\displaystyle 3x - 2y = 40[/tex]
* Parallel Lines have SIMILAR RATE OF CHANGES [SLOPES], so ⅔ and 3⁄2 remain the way they are.
I am joyous to assist you anytime.
(-6) x (3) = (3 x 6) x 3 =-1 x-1 =
Answer:
They are not equal? I don't get what you're trying to ask.
In which quadrant or on which axis would you find the point B(-8,0)?
Answer:
The x-axis, it would be between quadrant 2 and quadrant 3
Which number is greatest?
2.89 x 10^-8
1.997 x 10^2
8.9×10^-6.
5×10^-6
Answer:
1.997 x 10²
Step-by-step explanation:
The number with the highest exponent is the greatest value.
10² is bigger than 10⁻⁶ and 10⁻⁸, so 1.997 x 10² is your answer.
Which coordinate grid shows Point A at (0.75, −1.50)?
Answer:
Very bottom graph
Step-by-step explanation:
Go .75 units right (positive x) then go 1.5 units down (negative y)
Answer:
Your answer will be D.
Step-by-step explanation:
Coordinate grid shown from negative 2 to positive 2 on the x-axis and negative 2 to positive 2 on the y-axis in increments of 1 over 4. Only the whole numbers are labeled. A point A is shown at the intersection of 3 grid lines to the right of the y-axis and 6 grid lines below the x-axis.
if 3 popsicles cost $5.25. at this rate how much would 1 popsicle cost?
The sum of two numbers is 278. One number is 52 more than the other number. What are the two numbers
Answer:
The numbers are 165 and 113
Step-by-step explanation:
Let
x ----> one number
y ----> the other number
we know that
[tex]x+y=278[/tex] ----> equation A
[tex]x=y+52[/tex] ----> equation B
substitute equation B in equation A
[tex](y+52)+y=278[/tex]
solve for y
[tex]2y=278-52[/tex]
[tex]2y=226[/tex]
[tex]y=113[/tex]
Find the value of x
[tex]x=y+52[/tex]
[tex]x=113+52=165[/tex]
therefore
The numbers are 165 and 113
If h is an angle bisector of the given isosceles triangle, what is the measure of ∠a if ∠c = 55°?
Answer:
[tex]\angle a=35^o[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
An isosceles triangle has two equal sides and two equal interior angles
The angles opposite to the equal sides of an isosceles triangle are equal.
[tex]\angle b=\angle c[/tex]
we have
[tex]\angle c=55^o[/tex] -----> given problem
so
[tex]\angle b=55^o[/tex]
Remember that
The sum of the interior angles in any triangle must be equal to 180 degrees
[tex]\angle b+\angle c+2\angle a=180^o[/tex]
substitute the given values
[tex]55^o+55^o+2\angle a=180^o[/tex]
[tex]110^o+2\angle a=180^o[/tex]
[tex]2\angle a=180^o-110^o[/tex]
[tex]2\angle a=70^o[/tex]
[tex]\angle a=35^o[/tex]
2m- -3m + -15 =20 solve for m
Answer:
m=7
Step-by-step explanation:
2m-(-3m)+(-15)=20
2m+3m-15=20
5m-15=20
5m=20+15
5m=35
m=35/5
m=7
how to solve this please
Answer:
Step-by-step explanation:
Solve for x: 6/x = 4/8
Answer: x = 12
Step-by-step explanation:
[tex]\frac{6}{x}[/tex] = [tex]\frac{4}{8}[/tex]
cross multiply
4x = 6 × 8
4x = 48
divide through by 4
x = 12
-2/3, -4/5, -4/6, -5/4
The slope is -4/5
Step-by-step explanation:
We have to observe the graph to find two points to find slope.
The graph has two points
(-5,0) and (0, -4)
The formula for slope is given by:
[tex]m = \frac{y_2-y_1}{x_2-x_1}\\[/tex]
Here
(x1,y1) = (-5,0)
(x2,y2) = (0,-4)
Putting the values
[tex]m = \frac{-4-0}{0+5}\\=-\frac{4}{5}[/tex]
Hence,
The slope is -4/5
Keywords: slope, steepness
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3k-k+5k-7=7 solve for k
Answer:
k=2
Step-by-step explanation:
3k-k+5k-7=7
2k+5k=7+7
7k=14
k=14/7
k=2
Answer:
[tex] \: \: \: \: \: \: \: \: 3k - k + 5k - 7 = 7 \\ = > 8k - k = 7 + 7 \\ = > 7k = 14 \\ = > k = \frac{14}{7} \\ = > k = 2[/tex]
A sandbox has an area of 26 square feet . The length is 6 1/2 feet. What is the width of the sandbox
Answer:
The width of the sandbox is 4 feet
Step-by-step explanation:
Area = Length x Width
Fill in known values
26 sq ft = 6.5 ft x w
Divide by 6.5 on both sides
4 ft = w
Width = 4 ft
:)
y=6x-7 and find the x intercept
Answer:
x-intercept
= 7/6
= 1.16667
f(x) = 1/x
g(x) = x - 4
Can you evaluate (gof)(0)? Explain why or why
not.
(gof)(0) cannot be evaluated
Solution:
Given that,
[tex]f(x) = \frac{1}{x}\\\\g(x) = x - 4[/tex]
A composite function is denoted by (g o f) (x) = g (f(x)).
The notation g o f is read as “g of f”
Therefore, let us find whether (gof)(0) can be evaluated or not
To find (gof)(0):
(g o f) (x) = g (f(x))
Now substitute the given value of f(x)
[tex](g o f) (x) = g(\frac{1}{x})[/tex]
[tex]\text{ Substitute } x = \frac{1}{x} \text{ in } g(x) = x - 4[/tex]
[tex](g o f) (x) = \frac{1}{x} - 4[/tex]
Now to find (gof)(0), substitute x = 0
[tex](g o f) (x) = \frac{1}{0} - 4[/tex]
Since 1 divided by 0 is undefined, because any number divided by 0 is undefined
(gof)(0) cannot be evaluated
Answer:
You must evaluate the function f first.
Division by 0 is undefined.
The composition cannot be evaluated.
Step-by-step explanation:
A deck of cards contains 52 cards. These cards consist of four suits (hearts, spades, clubs, and diamonds) of each of the following: 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, and ace. If a card is chosen from a deck of cards, find the probability of drawing the 8 of spades.
The probability of drawing the 8 of spades from a deck of cards is 1/52, or approximately 0.0192, which can also be expressed as 1.92%.
Explanation:The probability of drawing the 8 of spades from a deck of cards is calculated as the number of favorable outcomes divided by the total number of possible outcomes. In this case, there is only 1 8 of spades card in the deck, and there are a total of 52 cards. Therefore, the probability is 1/52, or approximately 0.0192, which can also be expressed as 1.92%.
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