1. 8(2a+b)
2. 5(5g+3)
3. 8(3f+2)
The reverse of the distributive property involves factoring out the Greatest Common Factor (GCF) from the terms of the expression. For example, 16a + 8b becomes 8(2a + b), where 8 is the GCF.
The reverse of the distributive property involves factoring out the Greatest Common Factor (GCF) from each term in the expression to create an equivalent expression. Here's how it's done step-by-step:
Identify the GCF for all the terms in the expression.
Factor the GCF out of each term, which is essentially dividing each term by the GCF.
Write the factored expression in the form of the GCF multiplied by the remaining terms added together.
Applying this process:
For 16a + 8b, the GCF is 8, so the equivalent expression is 8(2a + b).
For 25g + 15, the GCF is 5, so the equivalent expression is 5(5g + 3).
For 24f + 16, the GCF is 8, so the equivalent expression is 8(3f + 2).
What function does this graph represent?
Answer:
I'm not sure if this is the answer answer but this what the graph is a parabola
The function represented by the graph is y = 1/4(x - 2)^2 + 1
What function does this graph represent?
From the question, we have the following parameters that can be used in our computation:
The graph
The graph is the graph of a quadratic function
By definition:
A quadratic function is represented as
y = a(x - h)^2 + k
Where
Vertex = (h, k)
From the graph, we have
Vertex = (2, 1)
So, we have
y = a(x - 2)^2 + 1
Using the point (0, 2) on the graph, we have
a(0 - 2)^2 + 1 = 2
4a + 1 = 2
4a = 1
a = 1/4
So, we have
y = 1/4(x - 2)^2 + 1
Hence, the function this graph represent is y = 1/4(x - 2)^2 + 1
−6⋅f(−3)−5⋅g(−7) = ?
Answer:
-12
Step-by-step explanation:
According to the graph, [tex]f(-3)=-3[/tex] and [tex]g(-7)=6[/tex]
When given the equation [tex]-6*f(-3)-5*g(-7)[/tex] we can substitute in the values on the graph that we have found.
[tex]-6*f(3)-5*g(-7)\\\\-6*(-3)-5*(6)\\\\18-30=-12[/tex]
Help! Using complete sentences, explain how to find the maximum value for each function and determine which function has the largest maximum y-value. F(x)=-4(x-6)^2+3.
Answer:
Final answer is that function g(x) has the largest maximum value, which is 6.
Step-by-step explanation:
Given function is [tex]F(x)=-4(x-6)^2+3[/tex].
Now we need to find about what is the maximum value of the given function [tex]F(x)=-4(x-6)^2+3[/tex] and explain the method about how did you find the maximum value.
Given function [tex]F(x)=-4(x-6)^2+3[/tex] looks similar to the quadratic function of the form [tex]f(x)=a(x-h)^2+k[/tex].
Comparing both we get: h=6, k=3
We know that maximum value occurs at the vertex where maximum value is given by "k"
Hence maximum value of the given function [tex]F(x)=-4(x-6)^2+3[/tex] is = 3
From graph we can clearly see that function g(x) has maximum height at 6.
So the final answer is that function g(x) has the largest maximum value, which is 6.
Scientists can estimate the depth of craters on the moon by studying the lengths of their shadows in the craters. Find the depth of a crater, if the shadow is estimated to be 400 m long and the angle of elevation of the sun is 48°.
It's a much more interesting problem when we have to estimate the shadow length from a photo.
The crater is a curvy bumpy surface, but let's approximate it as part of a sphere and just conflate the arc and chord length, so the 400 m shadow corresponds to a 400 m chord from the edge at the surface to the bottom.
The shadow as a chord forms a hypotenuse right triangle with the depth d being the leg opposite the 48 degree angle of the sun.
[tex] d = 400 \sin 48 \approx 297 \textrm{ m}[/tex]
Answer: 297 m
The depth is 297.26 m.
Height and distanceIt is the application of trigonometry.
Right angle triangleIt is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.
Given
The shadow is estimated to be 400 m long.
And the angle of elevation of the sun is 48°.
To findThe depth of a crater.
How to get the depth of a crater?Hypotenuse = 400m
Angle = 48°
The by the sine rule
[tex]\begin{aligned} \rm sin \theta &= \rm \dfrac{Depth}{Hypotenuse}\\\\\rm sin 48^o &= \rm \dfrac{depth}{400}\\\\\rm depth &= \rm sin 48^o * 400\\\\\rm depth &= 297.2579 \approx 297.26 \end{aligned}[/tex]
Thus, the depth is 297.26 m.
More about the height and distance link is given below.
https://brainly.com/question/10681300
The area of a rectangle is [tex]14ft^2[/tex], and the length of the rectangle is [tex]3ft[/tex] less than twice the width. Find the dimensions of the rectangle.
Answer:
So, Width = 7/2 or 3.5
Length = 4
Step-by-step explanation:
Area of rectangle = 14 ft^2
Let width of rectangle 2 = x
and Length of rectangle = 2x-3
Formula used for area of rectangle
Area = Length * Width
14 = (2x - 3) x
14 = 2x^2 - 3x
=> 2x^2 -3x -14 = 0
Solving the quadratic equation using factorization
-28 x^2 = -7x * -4x
2x^2 -7x + 4x -14 = 0
x (2x -7) +2(2x-7) = 0
(x+2) (2x-7) =0
=> x + 2 =0 and 2x -7 = 0
x = -2 and x = 7/2
Since width cannot be negative so, x= 7/2
Width= x = 7/2
Length = 2x -3 => 2(7/2) - 3
=> 7 -3
=> 4
So, Width = 7/2 or 3.5
Length = 4.
Length= 2width-3
Width=x
Length=2x+3
X(2x-3)=14
x must equal 3.5
Length=4
Width=3.5
2200 dollars is placed in an account with an annual interest rate of 7.25%. How much
will be in the account after 29 years, to the nearest cent?
Answer:
A = $2200(7.612) = $16,747.28
Step-by-step explanation:
You don't say whether this is simple interest or compound interest. I will assume you meant compound interest, for which the appropriate formula is
A = P(1 + r)^t, where P is the principal amount, r is the interest rate as a decimal fraction, and t is the time in years. Then:
A = $2200(1 + 0.0725)^29, or
A = $2200(1.0725)^29, or
A = $2200(7.612) = $16,747.28
The amount in the account after 29 years will be approximately $8484.64.
Explanation:To calculate the amount of money that will be in the account after 29 years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount ($2200 in this case), r is the annual interest rate (7.25% or 0.0725 as a decimal), n is the number of times interest is compounded per year (in this case, it's compounded annually, so n is 1), and t is the number of years (29 in this case). Plugging in the values, we get:
A = 2200(1 + 0.0725/1)^(1*29)
A = 2200(1.0725)^29
A ≈ $8484.64
Learn more about Compound interest here:https://brainly.com/question/14295570
#SPJ3
The graph of y =
[tex] \sqrt[3]{x} [/tex]
is reflected over the y-axis and then translated down 2 units to form f(x). Which is the graph of f(x)?
ANSWER
See attachment.
EXPLANATION
The given parent function is:.
[tex]y = \sqrt[3]{x} [/tex]
If this graph is reflected over the x-axis and then translated down 2 units to form f(x), then the f(x) has equation
[tex]f(x) = - \sqrt[3]{x} - 2[/tex]
The graph of this function is shown in the attachment.
Answer:
the second graph
Step-by-step explanation:
An animal shelter spends $5.50 per day to care for each bird and $8.50 per day to care for each cat. Anna noticed that the shelter spent $291.50 caring for birds and cats on Thursday. Anna found a record showing that there were a total of 41 birds and cats on Thursday. How many birds were at the shelter on Thursday?
Answer:
19
Step-by-step explanation:
We can solve this problem using a system of equation in two unknowns.
Let b = number of birds.
Let c = number of cats.
The care of a bird costs $5.50, so for b number of birds, the cost of care is 5.5b.
The care of a cat costs $8.50, so for c number of cats, the cost of care is 8.5c.
The total cost of care for the birds and cats is 5.5b + 8.5c.
The total cost of care is $291.50. This must equal the expression we have above, so we get our first equation.
5.5b + 8.5c = 291.5
The total number of birds and cats is b + c, but we are told it is 41, so our second equation is:
b + c = 41
We now have the following system of two equations in two unknowns.
5.5b + 8.5c = 291.5
b + c = 41
Rewrite the first equation.
Multiply both sides of the second equation by -8.5, and write it under the first equation. Then add the equations.
5.5b + 8.5c = 291.5
+ -8.5b - 8.5c = -348.50
--------------------------------------
-3b = -57
Divide both sides of the equation by -3.
b = 19
Answer: there were 19 birds
By defining the number of birds and cats as variables and setting up a system of equations, we solved for the number of birds to be 19.
Let's define the number of birds as b and the number of cats as c. From the problem, we have the following equations:
b + c = 41 (total number of birds and cats)
5.50b + 8.50c = 291.50 (total cost of caring for birds and cats)
To solve for the number of birds, we follow these steps:
Step 1: Express the number of cats in terms of birds.
From the first equation, we get:
c = 41 - b
Step 2: Substitute this expression into the second equation.
5.50b + 8.50(41 - b) = 291.50
Expand and simplify the equation:
5.50b + 348.50 - 8.50b = 291.50
Combine like terms:
-3b + 348.50 = 291.50
Step 3: Solve for b.
Subtract 348.50 from both sides:
-3b = 291.50 - 348.50
-3b = -57
Divide both sides by -3:
b = 19
Therefore, there were 19 birds at the shelter on Thursday.
Use the data set below to answer the following question.
2,4,7,2,3,7,9,3, 1,7
What is the mean absolute deviation (MAD) of this data set?
3.5
2.4
4.5
1.2
Answer:
2.4
Step-by-step explanation:
We have to find the mean first
[tex]Mean = \frac{Sum}{No.\ of\ values}\\ = \frac{2+4+7+2+3+7+9+3+1+7}{10}\\ = \frac{45}{10}\\ = 4.5[/tex]
Now we have to find deviations.
Note that the deviations are calculated by subtracting the mean from the value. The distance is always positive so the deviations will be positive
Value Deviation
2 2-4.5 = |-2.5| = 2.5
4 4-4.5 = |-0.5| = 0.5
7 7-4.5 = 2.5
2 2-4.5 = |-2.5| = 2.5
3 3-4.5 = |-1.5| = 1.5
7 7-4.5 = 2.5
9 9-4.5 = 4.5
3 3-4.5 = |-1.5| = 1.5
1 1-4.5 = |-3.5| = 3.5
7 7-4.5 = 2.5
The last step is to find the mean of deviations.
[tex]Mean\ of\ deviations = \frac{(2.5+0.5+2.5+2.5+1.5+2.5+4.5+1.5+3.5+2.5}{10}\\ = \frac{24}{10} \\=2.4[/tex]
The mean absolute deviation of given data set is 2.4 ..
If the original dimensions of a rectangular prism are doubled, how will the volume be affected? 2 times bigger 4 times bigger 6 times bigger 8 times bigger
The answer is 8 times bigger.
Hope this helps!
Answer:
2times bigger.
Step-by-step explanation:
Original volume of a rectangular prism = length × width × height
V = lwh... (1)
If the original dimension is doubled
New volume V2 = 2l × 2w × 2h
V2 = 2(lwh)...(2)
Taking the ratio of both volumes
V2/V = 2(lwh)/lwh
V2/V = 2
V2 = 2V
This shows that the new volume was two times bigger than the original volume
I need help with geometry, please Find area of kite.
Answer:
90 units²
Step-by-step explanation:
The area (A) of a kite is calculated as
A = [tex]\frac{1}{2}[/tex] × d₁ × d₂ ← diagonals
d₁ = 3 + 3 = 6 and d₂ = 20 + 10 = 30, hence
A = 0.5 × 6 × 30 = 90 units²
r(x)=x-3
s(x)= 4x²
write the expressions for (s+r)(x) and (s-r(x) and evaluate (s.r)(2)
What we are given:
r( x ) = x - 3
s( x ) = 4x²
We have to find:
( s + r )( x ) = ( x - 3 + 4x² )
→ 4x² + x - 3
( s - r )( x ) = ( x - 3 - 4x² )
→ -4x² + x - 3
For the last function, I am confused whether it is a multiplication or composite function, so I am going to do both.
Multiplication:
( x - 3 ( 4x² ))( 2 )
( 4x³ - 12x² )( 2 )
4(2)³ - 12(2)²
4(8) - 12(4)
32 - 48
→ -4
Composite function:
r(s(x))(2) = r(4x²) = 4x² - 3 = 4(2)² - 3 = 4(4) - 3 = 16 - 3
→13
Final answer:
The expressions for (s+r)(x) is 4x^2 + x - 3 and (s-r)(x) is 4x^2 - x + 3. The value of (s.r)(2) is 16.
Explanation:
To find the expression for (s+r)(x), we need to add the functions s(x) and r(x). Adding the two functions, we get (s+r)(x) = 4x^2 + (x-3). Simplifying this expression, (s+r)(x) = 4x^2 + x - 3.
To find the expression for (s-r)(x), we need to subtract the function r(x) from s(x). Subtracting the two functions, we get (s-r)(x) = 4x^2 - (x-3). Simplifying this expression, (s-r)(x) = 4x^2 - x + 3.
To evaluate (s.r)(2), we need to substitute 2 for x in the expression s(x) * r(x). Substituting 2 for x in the expression 4x^2, we get (s.r)(2) = 4(2)^2 = 16.
There are 13 bagels in a baker's dozen. Hillary,Mark, and Tam share the bagels equally. Will each friend get more than or fewer than 4 whole bagels? Explain.
Answer:
Each friend will get more than 4 whole bagels.
Step-by-step explanation:
First off, although the question asks for 13 bagels divided between 3 friends, let's use a number that results in a whole number when divided by 3, but is close to 13.
This number can be 12.
12 divided by 3 is 4, so each friend gets 4 bagels if there are a total of 12 bagels.
However, there are more than 12 bagels so we know that each of the the 3 friends will get more than 4 bagels each.
Each friend will get 4 whole bagels, with 1 bagel left over.
Explanation:In a baker's dozen, there are 13 bagels. Hillary, Mark, and Tam share the bagels equally. To determine if each friend will get more than or fewer than 4 whole bagels, we divide the total number of bagels by the number of friends.
13 bagels / 3 friends = 4 remainder 1
Each friend will get 4 whole bagels, with 1 bagel left over.
Division is one of the four basic operations of arithmetic. The other operations are addition, subtraction, and multiplication. What is being divided is called the dividend, which is divided by the divisor, and the result is called the quotient.
Learn more about Division here:https://brainly.com/question/33969335
#SPJ2
Find the value of x? I need help I don't understand what to do
Answer: (1) 120° (2) 6.5
Step-by-step explanation:
(1)
[tex]\dfrac{major\ arc-minor\ arc}{2}=intercepted\ angle\\\\\\\dfrac{(360-x)-x}{2}=60[/tex]
360 - 2x = 120
- 2x = -240
x = 120
(2)
2.5² + 6² = x²
6.25 + 36 = x²
42.25 = x²
6.5 = x
Two functions are shown below. For which value of x does f(x) = g(x)?
f(x) = 4x-4, g(x) = 2(3)^x-6
This question was on my Math 1 review so I think that the answer should be relatively uncomplicated. I looked around and only managed to find stuff dealing with logarithms, which I don't understand. Any help would be appreciated.
Answer:
x=0 and x=1
Step-by-step explanation:
4(1)-4=0
2(3)^(1)-6=0
4(0)-4=-4
2(3)^(0)-6=-4
A group surveyed a mix of people below and above 40 years old about whether or not they visit a dentist once a year. This table gives the survey results.
Visit Dentist Yearly Don’t Visit Dentist Yearly
Below 40 8 22
Above 40 17 13
Which table shows the relative frequency of people above 40 years old who do not visit a dentist once a year? Round your answers to the nearest hundredth.
Answer: is D
Visit Dentist Yearly Don’t Visit Dentist Yearly
Below 40 0.27 0.73
Above 40 0.57 0.43
Work: 8+22=30 17+13=30 turn into a fraction then simplify to get answer;
22/30 simp= 73.0 (0.73)
13/30 simp= 43.0 (0.43)
8/30 simp= 26.667 (0.27)
17/30 simp= 56.667 (0.57)
Answer with Step-by-step explanation:
Visit Dentist Yearly Don’t Visit Dentist Yearly
Below 40 8 22
Above 40 17 13
Relative frequency of people above 40 years old who do not visit a dentist once a year
=Number of people above 40 years old who do not visit a dentist yearly/Number of people above 40
=13/(17+13)
=13/30
=0.43
Hence, Relative frequency of people above 40 years old who do not visit a dentist once a year is:
0.43
PLEASE HELP Match each function formula with the corresponding transformation of the parent function y = - (x + 2)2. 1. y = - (x + 4)2 Reflected across the x-axis and the y-axis 2. y = - (x + 2)2 - 2 Translated right by 2 units 3. y = (x - 2)2 Translated left by 2 units 4. y = 2 - (x + 2)2 Translated down by 2 units 5. y = -x2 Translated up by 2 units 6. y = (x + 2)2 Reflected across the x-axis
So we are given the following function: [tex]y=-(x + 2)^{2}[/tex].
Before we can solve this problem, we need to know the following:
Given g (x) = f (x) + k; The graph of g(x) equals f(x) shifted k units vertically. If k > 0, the base graph shifts k units upward, and if k < 0, the base graph shifts k units downward. Given g(x) = f (x - k); The graph of g(x) equals f(x) shifted k units horizontally. If k > 0, the base graph shifts k units to the right, and if k < 0, the base graph shifts k units to the left.The reflection of the point (x,y) across the x-axis is the point (x,-y).The reflection of the point (x,y) across the y-axis is the point (-x,y).Know we can solve the problem!
1. [tex]y=-(x + 4)^{2}[/tex]. Translated left by 2 units.
2. [tex]y=-(x + 2)^{2} - 2 [/tex] Translated down by 2 units
3. [tex]y=(x - 2)^{2}[/tex] Reflected across the x-axis and the y-axis
4. [tex]y= 2-(x + 2)^{2}[/tex] Translated up by 2 units
5. [tex]y=-(x)^{2}[/tex] Translated right by 2 units
6. [tex]y=(x + 2)^{2}[/tex] y = (x + 2)2 Reflected across the x-axis
the area of a rectangle is represented by x^2 - 5x - 14. what are the dimensions?
Answer:
Step-by-step explanation:
A = x² - 5x - 14
Factor using AC method. Here, a = 1, b = -5, and c = -14.
ac = 1×-14 = -14
Factors of -14 that add up to -5 are -7 and 2.
A = (x - 7)(x + 2)
So the dimensions are x-7 and x+2.
The dimensions of the rectangle represented by the quadratic equation x² - 5x - 14 could be 7 and -2, but in a physical context we only consider the positive value 7.
Explanation:The area of a rectangle is given by multiplying its length and width. In this case, the area is expressed as a quadratic equation, x² - 5x - 14 = 0. Quadratic equations typically represent parabolas when graphed on a two-dimensional plot, but in this case, we're looking for linear dimensions of a rectangle. To find the dimensions of the rectangle, we need to factor this equation.
The factors of this quadratic equation are (x - 7) and (x + 2). Therefore, the two dimensions of the rectangle could be 7 and -2. However, in real-world scenarios, dimensions are often positive values due to physical constraints (you can't have a rectangle with negative length or width). So, normally, we would only consider the dimension of 7 (from the factor x - 7) as the real solution to this problem.
Learn more about Quadratic Equations here:https://brainly.com/question/30098550
#SPJ3
Which is the same as moving the decimal point 3 places to the right in a decimal number
Answer:
Multiplying the decimal number by 1000
Step-by-step explanation:
consider the number 12.2345.
For you to move the decimal point three places to the right, you have to multiply the number with 10³=1000
12.2345×1000= 12234.5
The decimal has moved from three places as it has skipped three places values to the right.
The choice which is the same as moving the decimal point 3 places to the right in a decimal number is; Multiplying the number by 1000.
Which is the same as moving the decimal point 3 places to the right in a decimal number?According to the task content;
We are required to determine which is the same as moving the decimal point 3 places to the right in a decimal number.Since, a decimal point movement one space to the right indicates a multiplication by 10, hence, it follows that the required multiplication is 1000.
Read more on decimal point;
https://brainly.com/question/11406179
#SPJ5
what is 11/7 as a mixed number
Answer:
1 4/7
Step-by-step explanation:
11/7 As A Mixed Number Would Be 1 And 4/7
A rectangular garden sits next to a house. Three sides of the garden are fenced, and the fourth side is the house. The length of the garden is 9 meters. A total of 21.5 meters of fencing is used. If w stands for the width of the garden in meters, which equation can be used to find its width?
A. 2w+9=21.5 C. 2w - 21.5 = 9
B. 2w + 18 = 21.5 D. 2w +21.5=18
the equation that can be used to find width is B
Answer:
It's a
Step-by-step explanation:
I did it
The coordinates G(7,3), H(9, 0), (5, -1) form what type of polygon?
an obtuse triangle
an acute triangle
an equilateral triangle
o a right triangle
Answer:
an acute triangle
Step-by-step explanation:
Given:
vertex 1 = (7,3)
vertex 2 = (9,0)
vertex 3 = (5,-1)
Now finding the length of each side of the triangle
Using distance formula, to find the length of side between vertex 1 and 2
d=[tex]\sqrt{(x2-x1)^{2}+ (y2-y1)^{2} }[/tex]
Putting values of x1=7 , x2=9, y1=3 and y2=0
d=[tex]\sqrt{(9-7)^{2}+ (0-3)^{2} }\\ =\sqrt{2^{2}+ 3^{2} }\\ =\sqrt{4+9} \\=\sqrt{13}[/tex]
Using distance formula, to find the length of side between vertex 1 and 3
Putting values of x1=7 , x2=5, y1=3 and y2=-1
d=[tex]\sqrt{(5-7)^{2}+ (-1-3)^{2} }\\ =\sqrt{2^{2}+ 4^{2} }\\ =\sqrt{4+16} \\=\sqrt{20[/tex]
Using distance formula, to find the length of side between vertex 2 and 3
Putting values of x1=9 , x2=5, y1=0 and y2=-1
d=[tex]\sqrt{(5-9)^{2}+ (-1-0)^{2} }\\ =\sqrt{4^{2}+ 1^{2} }\\ =\sqrt{16+1} \\=\sqrt{17[/tex]
Hence the three sides of triangle are:
√13, √20, √17
by Pythagoras theorem
if c^2= a^2 + b^2 then triangle is right triangle
if c^2> a^2 + b^2 then triangle is obtuse triangle
if c^2<a^2 + b^2 then triangle is acute triangle
Now let a=√13 b=√17 and c=√20 then:
a^2 + b^2 = 13+17
= 30
c^2=20
and 20 < 30 which means c^2<a^2 + b^2 then triangle is acute triangle !
To determine the type of triangle formed by the points G(7,3), H(9, 0), and (5, -1), one needs to calculate the lengths of the sides using the distance formula and then apply the Pythagorean theorem to determine if it is a right, acute, or obtuse triangle.
Explanation:The coordinates G(7,3), H(9, 0), and (5, -1) can form a triangle on a Cartesian plane, and we need to determine the type of triangle they form. To solve this problem, we need to calculate the lengths of the sides of this triangle using the distance formula, which is √((x2-x1)² + (y2-y1)²) for two points (x1, y1) and (x2, y2). Once we have all three sides, we can determine the type of triangle by applying the Pythagorean theorem, where the square of the length of the longest side (the hypotenuse 'c') is equal to the sum of the squares of the other two sides (a and b).
By applying the Pythagorean theorem, if the sum of the squares of the two shorter sides equals the square of the longest side, the triangle is a right triangle. If the square of the longest side is greater than the sum of the squares of the other two sides, it is an obtuse triangle. And if it’s less, the triangle is an acute triangle.
Given the way the coordinates are arranged in the fragmented information, it appears the triangle they form is relevant to understanding relationships between sides and angles. The mnemonic SOHCAHTOA is often used to remember the ratios of sides in a right triangle. Since the information for determining the lengths of the sides directly is not fully provided, we can't explicitly state the type of triangle formed by the points G(7,3), H(9, 0), and (5, -1) without further calculation.
PLease Help i need it
What side length would be possible for a triangle if you already know the other two lengths are 19cm and 32cm
Please explain step by step
Answer:
13 < n < 51
Explanation:
Basically to find the lowest possible length, all you need to do is subtract the lower number from the higher number (32 - 19), and to find the greatest possible length, add the lower number and the higher number (32 + 19). Then you'd plug it in to this inequality: a < n < b, a being the difference, and b being the sum. But, if the triangle were a right triangle that would be a whole different story.
PLEASE HELP
find the vertex of f(x)=x^2+2x+3 (make sure you show your work)
Answer:
(- 1, 2)
Step-by-step explanation:
Given a quadratic in standard form y = ax² + bx + c : a ≠ 0
Then the x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
f(x) = x² + 2x + 3 ← is in standard form
with a = 1 and b = 2, hence
[tex]x_{vertex}[/tex] = - [tex]\frac{2}{2}[/tex] = - 1
Substitute x = - 1 into f(x) for corresponding value of y
f(- 1) = (- 1)² + 2(- 1) + 3 = 1 - 2 + 3 = 2
vertex = (- 1, 2 )
match each function with its inverse function. use function composition to determine your answers.
QUESTION 1
[tex] \boxed {f(x) = 2x + 6 \to \: g(x) = \frac{1}{2}x - 3 } [/tex]
The reason is that:
[tex]g(f(x)) = 2( \frac{1}{2} x - 3) + 6[/tex]
Expand:
[tex]g(f(x)) = x - 6+ 6 [/tex]
[tex]g(f(x)) = x[/tex]
QUESTION 2
[tex]\boxed {f(x) =3 - 2x \to \: g(x) = - \frac{1}{2}(x - 3)} [/tex]
The reason that
[tex]g(f(x)) = - \frac{1}{2} (3 - 2x - 3)[/tex]
[tex]g(f(x)) = - \frac{1}{2} (- 2x )[/tex]
[tex]g(f(x)) =x[/tex]
QUESTION 3
[tex]\boxed {f(x) = \sqrt[3]{3x}+ 2 \to \: g(x) = \frac{ {(x - 3)}^{3} }{3} } [/tex]
The reason is that:
[tex]f(g(x)) = \sqrt[3]{ \frac{3 {(x - 2)}^{3} }{3} } + 2[/tex]
[tex]f(g(x)) = x-2 + 2[/tex]
[tex]f(g(x))=x[/tex]
QUESTION 4
[tex]\boxed {f(x)=3\sqrt[3]{x + 2} \to \: g(x) = \frac{1}{27} {x}^{3} - 2} [/tex]
The reason is that
[tex]f(g(x)) = 3 \sqrt[3]{ \frac{1}{27} {x}^{3} - 2 + 2} [/tex]
[tex]f(g(x)) = 3 \sqrt[3]{ \frac{1}{27} {x}^{3} } [/tex]
[tex]f(g(x)) = 3 \times \frac{1}{3} x[/tex]
[tex]f(g(x)) =x[/tex]
Write 1,000 as a power of 100
Answer:
10 or 100
Step-by-step explanation:
Answer:
100^1,000 if that's what you mean or 100 ^10 to make 1,000
Step-by-step explanation:
IF RIGHT PLZ MARK BRAINLIEST!! PLZZZ!!!!!!!!!!!!!
Type an inequality statement using the < or > for the inequality symbols solve for x 6x-11-13x<7-5x
Answer:
-9 < x
Step-by-step explanation:
6x-11-13x<7-5x
Combine like terms
-11-7x<7-5x
Add 7x to each side
-11-7x+7x<7-5x+7x
-11 < 7+2x
Subtract 7 from each side
-11-7 < 7-7+2x
-18 < 2x
Divide by 2
-18/2 < 2x/2
-9 < x
3. What’s the answer to this question?
Answer:
Opt B. y=5-3x
Step-by-step explanation:
We need to write the given equation in slope-intercept form, so we can obtain the slope and the 'y' axis intercept point.
To do this, we need to isolate 'y' variable with a possitive sign, hence we perform the following operation:
Subtraction of -5 in both sides of equality sign.
-y=3x-5
Lets multiply by -1 the equation from above:
y= 5-3x.
From the above we can find the slope, is the coefficient of x. in this case -3
And the y-intercept point is 5.
An inconsistent linear system has _ solutions
Answer:
zero im pretty sure
Step-by-step explanation:
Answer:
An inconsistent linear system has no solution(s).
Step-by-step explanation:
Just took the test.
The first equation in the following system gives the company's cost of making x purses. The second equation gives the company's income for selling x purses.
3111-04-10-10-07
You used substitution to obtain the equation
0 = -0.01x2-10x+1,989 from the system.
What are the solutions to the system of equations?
(-23,400, 3,400) and (-1,170,170)
(-1,170, -23,400) and (170, 3,400)
(274, 726) and (5,480, 14,520)
(274, 5,480) and (726, 14,520)
The solution (-1170, -23,400) should be eliminated in the context of this situation.
The company will break even when its cost of making x purses equals its income for selling x purses. The company must make and sell purses to break even. (Just need help with the last part of this.)
1st Answer: B.) (-1,170, -23,400) and (170, 3,400)
2nd Answer: 170
Answer:
that answer is verified 100% correct
Step-by-step explanation: