Step-by-step explanation:
Parent function f(x) = x
g(x)= -3(x-4) + 1
If any number added or subtracted with x then graph moves left or right
Here 4 is subtracted from x, so graph move 4 units to the right
If any number added or subtracted at the end then graph move up or down
Here 1 is added at the end, so graph move 1 unit up.
g(x) = -f(x), for negative sign the graph reflects across x axis
We have negative sign at first, so the graph reflects over x axis
The graph of [tex]\( g(x) \)[/tex] is the result of these transformations applied to the graph of the parent function [tex]\( f(x) \)[/tex].
The sequence of transformations that transforms the graph of the parent function [tex]\( f(x) = x \)[/tex] into the graph of the function [tex]\( g(x) = -3(x-4)+1 \)[/tex] involves a reflection across the x-axis, a horizontal shift, a vertical stretch, and a vertical shift.
1. Reflection across the x-axis: The negative sign in front of the function[tex]\( g(x) \)[/tex]indicates a reflection across the x-axis. This means that for every point \( (x, y) \) on the graph of [tex]\( f(x) \)[/tex], there will be a corresponding point [tex]\( (x, -y) \)[/tex] on the graph of [tex]\( g(x) \)[/tex].
2. Horizontal shift: The expression [tex]\( (x-4) \)[/tex] inside the function [tex]\( g(x) \)[/tex]indicates a horizontal shift to the right by 4 units. This means that every point on the graph of [tex]\( f(x) \)[/tex] is moved 4 units to the right along the x-axis to get the graph of [tex]\( g(x) \).[/tex]
3. Vertical stretch: The coefficient 3 in [tex]\( -3(x-4) \)[/tex] indicates a vertical stretch by a factor of 3. This means that for every point [tex]\( (x, y) \)[/tex] on the graph of the reflected function[tex]\( -f(x) \)[/tex], the y-coordinate is multiplied by 3 to get the corresponding point [tex]\( (x, 3y) \)[/tex] on the graph of [tex]\( g(x) \)[/tex].
4. Vertical shift: Finally, the[tex]\( +1 \)[/tex] at the end of the function [tex]\( g(x) \)[/tex]indicates a vertical shift upwards by 1 unit. This means that every point on the graph of [tex]\( -3f(x-4) \)[/tex] is moved 1 unit up along the y-axis to get the graph of [tex]\( g(x) \).[/tex]
Putting it all together, the sequence of transformations is as follows:
- Start with the parent function [tex]\( f(x) = x \).[/tex]
- Reflect the graph across the x-axis to get [tex]\( -f(x) \).[/tex]
- Shift the graph 4 units to the right to get [tex]\( -f(x-4) \).[/tex]
- Stretch the graph vertically by a factor of 3 to get [tex]\( -3f(x-4) \).[/tex]
- Shift the graph 1 unit upwards to get [tex]\( -3f(x-4) + 1 \),[/tex] which is the function [tex]\( g(x) \)[/tex].
Therefore, the graph of [tex]\( g(x) \)[/tex] is the result of these transformations applied to the graph of the parent function [tex]\( f(x) \)[/tex].
There are 90 fith-grade students going on a feild trip. Each student gives the teacher $9.25 to cover admission to the theater and for lunch. Admission for all the students will cost $315, and each student will get an equal amount to spend on lunch. How much will each fifth grader get to spend on lunch?
Answer:
they each get $5.75 for lunch
Step-by-step explanation:
9.25 x 90 students = 832.50
832.50 -315 = 517.50
517.50 / 90 = 5.75
What is the quotient of
y-5\sqrt{2y^2-7y-15}
A. 2y + 3
B. 2y − 3
C. 2y − 17y R −70
D. 2y − 17y R 70
Answer:
None of these
Step-by-step explanation:
y-5\√(2y2 - 7y -15)
On simplifying 2y2 - 7y -15, we get
2y2 – (10-3)y -15
= 2y2 – 10y -3y-15
= 2y(y-5)-3(y-5)
= (2y-3)(y-5)
On squaring nominator and denominator we get
(y-5)2/(2y-3)(y-5)
= (y-5)/(2y-3)
So the quotient becomes, 5/2
While the remainder becomes 2.5
Answer:
I think its A
Step-by-step explanation:
solve and simplify, typing the final answer as a fraction 1/4 ÷ 3/8
[ Answer ]
2 / 3
[ Explanation ]
1 * 8 / 4 * 3
8 / 12
Simplify:
2 / 3
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your network wants you. to cut your expenses per episode. they have given you a budget of $85,134 for the next 6 episode. how much do you have to spend per episode?
Amelia and Brianna work at a furniture store. Amelia is paid $240 per week plus 6% of her total sales in dollars, xx, which can be represented by g(x)=240+0.06xg(x)=240+0.06x. Brianna is paid $130 per week plus 8.5% of her total sales in dollars, xx, which can be represented by f(x)=130+0.085xf(x)=130+0.085x. Determine the value of xx, in dollars, that will make their weekly pay the same.
Answer:
x = $4400
Step-by-step explanation:
If we want their pay to be the same, the equations have to be equal
g(x)=240+0.06x = f(x)=130+0.085x
240 + .06x = 130+0.085x
Subtract .06x from each side.
240 + .06x - .06x = 130+0.085x-.06x
240 = 130 +.025x
Subtract 130 from each side
240-130 = 130-130 +.025x
110 = .025x
Divide each side by .025 to isolate x
110/.025 = .025x/.025
4400 =x
i dont understand this help me :( What is the equation of a line with a slope of 3 and a point (3, 1) on the line?
Express the equation in the form of y=mx+b where m is the slope and b is the y-intercept.
[tex]\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{1})~\hspace{10em} slope = m\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-1=3(x-3) \\\\\\ y-1=3x-9\implies y=3x-8[/tex]
At the beginning of the week Fayez writes down the mileage of his limo at 2529 at the end of the week the mileage is 2834, Fayez knows he used 75.2 litres of petrol during this week. The handbook states the limo uses 1 gallon of petrol for every 20 miles. Fayez wants to know if his limo uses 1 gallon of petrol for every 20 miles that week. 1 gallon = 4.54 litres . Did his limo use 1 gallon of petrol every 20miles that week. Show your answer clearly
Answer:
No. It used 1 gallon in 18.41 miles.
Step-by-step explanation:
He travelled 2834 - 2529 = 305 miles.
So his consumption is 305 / 75.2 = 4.056 miles/litre.
This equals 4.056*4.54 = 18.41 miles / gallon.
So this is less than the 1 gallon every 20 miles stated by the handbook.
Answer: His limo used 1 gallon fuel for 18.4136 miles.
Step-by-step explanation:
Fayez covered distance:
2834 - 2529 = 305 miles.
He used fuel = 75.2 litres
75.2/4.54 = 16.5638 gallons petrol used.
His limo covered distance / total petrol used = 305 miles / 16.5638 gallons petrol = 18.4136 miles per gallon.
That is less than 20 miles per gallon
How do you solve for a²+b²=289 when b+a=23
Answer:
1 Use Product Rule: {x}^{a}{x}^{b}={x}^{a+b}x
a
x
b
=x
a+b
{a}^{2}+bb=289a
2
+bb=289
2 Use Product Rule: {x}^{a}{x}^{b}={x}^{a+b}x
a
x
b
=x
a+b
{a}^{2}+{b}^{2}=289a
2
+b
2
=289
3 Subtract {b}^{2}b
2
from both sides
{a}^{2}=289-{b}^{2}a
2
=289−b
2
4 Take the square root of both sides
a=\pm \sqrt{289-{b}^{2}}a=±√
289−b
2
5 Rewrite 289-{b}^{2}289−b
2
in the form {a}^{2}-{b}^{2}a
2
−b
2
, where a=17a=17 and b=bb=b
a=\pm \sqrt{{17}^{2}-{b}^{2}}a=±√
17
2
−b
2
6 Use Difference of Squares: {a}^{2}-{b}^{2}=(a+b)(a-b)a
2
−b
2
=(a+b)(a−b)
a=\pm \sqrt{(17+b)(17-b)}a=±√
(17+b)(17−b)
What is the sum of 4a^2 − 7a − 5 and −8a^2 − 2a + 7?
5. State whether the number 91 is prime, composite, or neither.
Answer:
91 is a composite number
Step-by-step explanation:
A prime number is the positive number, which has factors 1 and itself.
Example : 1,3,5,7
Clearly 91 is not a prime number, as its factors are:
91 = 1,7,13,91
It has more than 2 factors (1 and itself), hence 91 is a composite number.
Composite number is the number which has factors other than 1 and itself.
Answer:
91 is composite
Step-by-step explanation:
its factors are 1, 7, 13, 91
the product of p and 9
Answer:
The answer is p · 9
Step-by-step explanation:
Product means multiplication
Answer:
The answer is p · 9
but, on gradpoint the answer is 9p
Step-by-step explanation:
If quadrilateral ABCD is congruent to quadrilateral EFGH, then what corresponding side is congruent to side EF? (5 points)
Answer:
Side AB
Step-by-step explanation:
Draw two congruent quadrilaterals.
Label the sides of one A,B,C,and D.
Label the sides of the other E,F,G,and H
Because the sides match up with the order in which they appear in if they are congruent, The first two letters(E and F) should be equivalent to the first two letters of the other shape(A and B).
Please help me with number 6
The answer is C) $250
Answer:
The answer is 250 dollars. to find this do 25 times 1000. the placement is 25 over 100 and x as in the amount were trying find over 1000.
Step-by-step explanation:
If 9 is added to twice a number and this sum is multiplied by 6, the result is the same as if the number is multiplied by 7 and 14 is added to the product. What is the number?
Answer:
The number is -1.
Step-by-step explanation:
Let the number be represented by n.
Then "9 is added to twice a number and this sum is multiplied by 6" is represented by 2n + 9, and
" the number is multiplied by 7 and 14 is added to the product" is
7n + 14.
Then the complete equation is 2n + 9 = 7n + 14.
We must solve this for n. To accomplish this, subtract 2n from both sides, obtaining 9 = 5n + 14. Then subtract 14 from both sides, obtaining
-5 = 5n. Then n must be -1.
Answer:
The number is -8
Step-by-step explanation:
Developing an equation
Read these phrases a little a time.
9 is added to twice a number = 2x + 9This sum is multiplied by 6 = 6* sum = 6 * (2x + 9) Note the brackets.is the same thing as means = the number multiplied by 7 = 7xand 14 is added to the product 7x + 14So what you have is equation: 6*(2x + 9) = 7x + 14Solution
6*(2x + 9) = 7x + 14 Remove the brackets on the left12x + 54 = 7x + 14 Subtract 14 from both sides12x + 54 - 14 = 7x + 14 - 14 Collect terms12x + 40 = 7x Subtract 12x from both sides.12x - 12x + 40 = 7x - 12x Combine40 = -5x Divide by - 540/-5 = x Do the division- 8 = x50% of one-twentieth of the product of 12 and 5z + 5.
Final answer:
To simplify 50% of one-twentieth of the product of 12 and 5z plus 5, you first calculate the product (60z), take one-twentieth (3z), find 50% of that (1.5z), and then add 5 to get the simplified expression 1.5z + 5.
Explanation:
The question asks to simplify the expression 50% of one-twentieth of the product of 12 and 5z plus 5. Here are the steps to simplify this expression:
Firstly, calculate the product of 12 and 5z, which is 60z.
Then, find one-twentieth of this product, which is 60z / 20 = 3z.
50% of 3z is 1.5z.
Finally, add 5 to 1.5z, which gives you 1.5z + 5 as the simplified expression.
So, the simplified expression is 1.5z + 5.
50% of one-twentieth of the product of (12) and[tex]\(5z + 5\) is \( \frac{3z}{2} + \frac{3}{2} \).[/tex]
To calculate 50% of one-twentieth of the product of [tex]\(12\) and \(5z + 5\)[/tex], we'll follow these steps:
Step 1: Calculate the product of [tex]\(12\) and \(5z + 5\)[/tex].
[tex]\[ \text{Product} = 12 \times (5z + 5) \][/tex]
Step 2: Calculate one-twentieth of the product.
[tex]\[ \text{One-twentieth of the product} = \frac{\text{Product}}{20} \][/tex]
Step 3: Calculate 50% (or half) of one-twentieth of the product.
[tex]{50% of one-twentieth of the product}[/tex] = [tex]\frac{1}{2} \times \frac{\text{Product}}{20} \][/tex]
Now, let's perform the calculations step by step:
Step 1: Calculate the product of [tex]\(12\) and \(5z + 5\):[/tex]
[tex]\[ \text{Product} = 12 \times (5z + 5) \][/tex]
[tex]\[ = 12 \times 5z + 12 \times 5 \][/tex]
[tex]\[ = 60z + 60 \][/tex]
Step 2: Calculate one-twentieth of the product:
[tex]\[ \text{One-twentieth of the product} = \frac{60z + 60}{20} \][/tex]
[tex]\[ = \frac{60z}{20} + \frac{60}{20} \][/tex]
[tex]\[ = 3z + 3 \][/tex]
Step 3: Calculate 50% of one-twentieth of the product:
{50% of one-twentieth of the product} =[tex]\frac{1}{2} \times \left(3z + 3\right) \][/tex]
[tex]\[ = \frac{1}{2} \times 3z + \frac{1}{2} \times 3 \][/tex]
[tex]\[ = \frac{3z}{2} + \frac{3}{2} \][/tex]
So, 50% of one-twentieth of the product of (12) and[tex]\(5z + 5\) is \( \frac{3z}{2} + \frac{3}{2} \).[/tex]
Solve using substitution
x=2y-6
y= -3x+17
Answer:
(x, y) = (4, 5)
Step-by-step explanation:
given the 2 equations
x = 2y - 6 → (1)
y = - 3x + 17 → (2)
Either substitute x = 2y - 6 into (2) or y = - 3x + 17 into (1)
substituting y = - 3x + 17 into (1)
x = 2(- 3x + 17) - 6
x = - 6x + 34 - 6
x = - 6x + 28 ( add 6x to both sides )
7x = 28 ( divide both sides by 7 )
x = 4
substitute x = 4 into (2)
y = - 12 + 17 = 5
solution is (4, 5 )
Answer please ?!?!?!
Answer: -9
Step-by-step explanation: -91/6 ≈ -9.167
21/3 ≈ 2.33333
-17/8 ≈ -1.875
-9.167 + 2.3333 + -1.875 = -8.71
Rounded, the answer is -9.
a fruit stand has to decide what to charge for their produce. They need $10 for 4 apples and 4 oranges. They also need $12 for 6 apples and 6 oranges. We put information into a system of linear equations.
Answer:
X = apple
y = orange
4x + 4y = 10
6x + 6y = 12
Step-by-step explanation:
Answer:
4a+4r = 10
6a + 6r = 12
No solutions
Step-by-step explanation:
a = cost of the apple
r = cost of the orange
4a+4r = 10
6a + 6r = 12
Divide the first equation by 2 and the second equation by 6
2a+2r = 5
a +r = 2
Multiply the second equation by -2 so we can eliminate a
-2a -2r = -4
Add the first equation
2a+2r = 5
-2a -2r = -4
---------------------
0 = 1
This system is inconsistent and has no solutions
You are making sets of pens and pencils to sell. You want each set to contain the same combination of pens and pencils. You have 28 pens and 80 pencils, and you want to use them all. What is the greatest number of these sets you can make?
The greatest number of sets of pens and pencils that can be made, using all of the given 28 pens and 80 pencils in each set, is 4. Each set would contain 7 pens and 20 pencils.
Explanation:In the problem, we are looking to find the Greatest Common Divisor (GCD), which is the greatest number that can evenly divide both the number of pens (28) and the number of pencils (80). The GCD between 28 and 80 is 4.
Thus, the most sets of pens and pencils you can make would be equal to the GCD, which in this case is 4.
This means you can put together 4 sets with an equal number of pens and pencils in each set. In each of these sets, there would be 7 pens (28 pens ÷ 4 sets) and 20 pencils (80 pencils ÷ 4 sets).
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Final answer:
To maximize the number of sets with 28 pens and 80 pencils, find the greatest common divisor and divide the total by it. You can create 27 sets of 4 pens and 10 pencils each.
Explanation:
To find the greatest number of sets you can make with 28 pens and 80 pencils, you need to determine the highest common factor of the two quantities.
Calculate the greatest common divisor (GCD) of 28 and 80, which is 4.
Divide the total number of pens and pencils by the GCD: (28 + 80) ÷ 4 = 27.
You can make 27 sets, each consisting of 4 pens and 10 pencils.
Will give brainliest please help ASAP
Answer:
D
Step-by-step explanation:
y>-3x+1 Negative slope
y<x+2 Positive slope
< or > have dotted line
< or > have a solid line
> or > means solutions are above the line
< or < means solutions are below the line
The one with negative slope has a dotted line and solutions above it.
The one with positive slope has a solid line and solutions below it.
D-I are the measurements of the lengths of the sides of triangles. Identify the types of
triangles
d. 45 cm 61 cm 60 cm e. 30 cm, 31cm, 30 cm f. 4 cm, 5ft, 4 cm
g. 89mm, 89mm, 89mm h. 9 in, 5in, 3 in i. 22cm, 22cm, 22in
J-O are the measurements of the angles of triangles. Identify the type of triangle.
j. 900, 350, 550 k. 600, 600, 600 l. 700, 550, 550
m. 350, 400, 1000 n. 460, 460, 440 o. 1200, 300, 300,
Answer:
The sum of the interior angles of a triangle is 180 degrees.
d. Scalene
e. Isosceles
f. Isosceles
g. Equilateral
h. Scalene
i. Equilateral
j. Right
l. Acute
m. Obtuse - doesn't add to 180 not a triangle
n. Acute - doesn't add to 180 not a triangle
o. Obtuse
Step-by-step explanation:
The interior angles of a triangle add to 180 degrees. There are two ways we classify triangle by side lengths and angle measures.
Side lengths: Compare the side lengths and see if any are equal to determine the type.
Scalene: 3 different lengthsIsosceles: 2 equal lengths and 1 differentEquilateral : 3 equal sidesAngle Measures: Compare the angles measures to 90 degrees.
Right: If one angle is equal to 90Acute: All angles are less than 90 degreesObtuse: One angle is greater than 90 degreesexplain whether a quadratic function can have both a maximum value and a minimum value
A quadratic function can not have a maximum and minimum value. It can only take on one of those. The quadratic only makes one turn, so if the quadratic opens upwards, there is a minimum. If the quadratic opens downwards, there is a maximum.
A quadratic function can have either a maximum value or a minimum value, but not both.
Explanation:A quadratic function can have either a maximum value or a minimum value, but not both. Whether it has a maximum or minimum value depends on the coefficient of the quadratic term (a) in the function. If a is positive, the graph of the quadratic function opens upwards and has a minimum value. If a is negative, the graph opens downwards and has a maximum value.
For example, the function y = x² has a minimum value of 0 at the vertex of the parabola, while the function y = -x^2 has a maximum value of 0 at the vertex.
Therefore, a quadratic function cannot have both a maximum value and a minimum value.
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Please answer with calculations
Answer:
Step-by-step explanation:
Given that a storage rack has dimensions as 25x12x5 ft.
Box has dimensions as 15x8x10 inches
Volume of each box = 15(8)(10) = 1200 inches = 1200x12^(-3) feet^3
Volume of 5000 boxes = 5000 (1200x12^(-3) ) = 3472.22 cubic feet
Volume of storage rack = 25(12)(5) = 1500 cubic feet
Volume of 25 storage racks 1500(25) = 37500 cubic feet.
SInce storage racks have sufficient volume it is concluded that enough storage is there.
Answer:
Yes, we have enough storage space.
Step-by-step explanation:
25 storage racks that are:
Length: Lsr = 25 ft = 25 ft (12 in / 1 ft) → Lsr = 300 in
Width: Wsr = 3 ft = 3 ft (12 in / 1 ft) → Wsr = 36 in
Height: Hsr = 12 ft = 12 ft (12 in / 1 ft) → Hsr = 144 in
5000 boxes 15x8x10 in
Length: Lb = 15 in
Width: Wb = 8 in
Height: Hb = 10 in
In the length of each storage rack we can put:
Nl=Lsr/Lb=300 in / 15 in → Nl = 20
In the width of each storage rack we can put:
Nw=Wsr/Wb=36 in / 8 in = 4.5 → Nw = 4
In the height of each storage rack we can put:
Nh=Hsr/Hb=144 in / 10 in = 14.4 → Nh = 14
Then we can put in each storage rack:
N = Nl Nw Nh = (20)(4)(14) → N=1,120 boxes
And we have 25 storage racks, then we can storage in total:
Nt=25N=25(1,120)→Nt=28,000 boxes
And we have 5,000 boxes, then we have enough storage space
I don’t understand all 3 of them
Suppose f(x)=x2 Find the graph of f (x)+1
You would vertically shift the function up a unit, making it clear that the answer should be graph 3.
Use the image below, red is the original function, and blue is the new function.
What is the remainder when the polynomial f(x)=3x^3-4x^2+2x+8 is divided by (x-5)
Answer:
remainder = 290
Step-by-step explanation:
[tex]\frac{3x^3-4x^2+2x+8}{x-5}[/tex]
= 3x² + 11x + 57 + [tex]\frac{290}{x-5}[/tex]
quotient = 3x² + 11x + 57 and remainder = 290
When solving for x what would (8x-46) + (10x-8)
Answer:
18x - 54 :) :( :) :)jordan is chopping wood for the winter. for 10 days on a row he follows the same process: in the morning he chops 20 pieces of wood and in the evening he chops an additional 30 pieces of wood on the 11th day jordan chops only 5 pices of wood write a numerical expression with parentheses for the total number of pieces of wood jordan chopped. (do not simplify your expression)
you get to pick 8 of your 12 favorite songs to put on a cd . how many ways 8 songs be arranged from a choice of 12 songs
Linda received a $ 90 gift card for a coffee store. She used it in buying some coffee that cost $ 7.63 per pound. After buying the coffee, she had $ 51.85 left on her card. How many pounds of coffee did she buy?
Answer:
5 pounds
Step-by-step explanation:
:'>
Answer:
She bought 5 pounds of coffee.
Step-by-step explanation: