Answer:
right 2, up 3
Step-by-step explanation:
The original function is:
[tex]f(x) = x^2[/tex]
Translated to:
[tex]g(x)=(x-2)^2+3[/tex]
Lets look at the constants that are added or subtracted to determine the transformation.
As -2 is is added to x (grouped with x), the transformation is a horizontal transformation. The shift is of two to the right.
As +3 is not grouped with x, the transformation is vertical. The shift is vertical shift of 3 to upward direction.
So the correct answer is:
right 2, up 3 ..
y= -3/4x+3 and y=-12
Answer:
x = 20, y = -12Step-by-step explanation:
[tex]y=-\dfrac{3}{4}x+3\ and\ y=-12\\\\\text{Substitute the value of y to the first equation:}\\\\-12=-\dfrac{3}{4}x+3\qquad\text{multiply both sides by 4}\\\\-48=-3x+12\qquad\text{subtract 12 from both sides}\\\\-60=-3x\qquad\text{divide both sides by (-3)}\\\\20=x\to x=20[/tex]
Answer:
x = 20, y = -12
Step-by-step explanation:
y= -3/4x+3 and y=-12
x = 20, y = -12
Can someone please help me ..
Answer:
The mean of pictures is 2
Step-by-step explanation:
To find the mean we add up all the pictures then divide it by the amount of newspapers, there are 10 and 5 newspapers. 10/5=2.
For the graph of function f shown below, which of the following is true?
Answer:
A
Step-by-step explanation:
Because it touches the x axis 3 times as shown in your graph
Hope it helps you..☺
EMERGENCY!!
What are the solutions to the equation (x-6)(X + 8) = 0?
x= -6 or x = 8
x=-6 or x = -8
x = 6 or x = -8
x= 6 or x = 8
The ratio of the height of two similar cylinders is 4 to 3 What is the ratio of their volumes
Answer:
64 : 27
Step-by-step explanation:
When using scale factors
Length = scale factor
Area = scale factor squared
Volume = scale factor cubed
The ratio is 4:3
The ratio of the volume is 4^3 : 3^3
64 : 27
I NEED HELP ASAP
The graphs of f(x) = –2x and
g(x) = (1/2)^x are shown.
What are the solutions to the equation
-2x = (1/2)^x ?
Select each correct answer.
-2, -1, 2, 4
Answer:
I have not the slightest clue but there's an app called cam calc and I swear its the best
Answer:
-2!
Step-by-step explanation:
im just finished this exact test and i swear thats the right answer!!
Find the x-intercepts of the parabola with
vertex (-1,-108) and y-intercept (0,-105).
Write your answer in this form: (x1,71), (x2,y2).
If necessary, round to the nearest hundredth.
Answer:
The x-intercept are (-7 , 0) and (5 , 0)
Step-by-step explanation:
* Lets revise the general form of the equation of the parabola
- The general form of the equation of the parabola is:
y = ax² + bx + c , a , b , c are constant
- The y-intercept is c, because the parabola intersect the y-axis at
point (0 , c)
- The x-coordinate of the vertex point is -b/2a
* Now lets solve the problem
∵ The general form of the equation of the parabola is y = ax² + bx + c
∵ The y-intercept is -105
∴ c = -105
∴ y = ax² + bx - 105
∵ The vertex point is (-1 , -108)
∴ The x-coordinate of the vertex of the parabola = -1
∵ The x-coordinate of the vertex of the parabola = -b/a
∴ -b/2a = -1 ⇒ using cross multiplication
∴ -b = -2a ⇒ multiply two sides by -1
∴ b = 2a
- Substitute the value of b in the equation
∴ y = ax² + 2ax - 105
- Substitute the value of x , y in the equation by the coordinates of
the vertex point
∵ The vertex point lies on the parabola
∴ put x = -1 and y = -108
∴ -108 = a(-1)² + 2a(-1) - 105
∴ -108 = a - 2a - 105 ⇒ add the like term
∴ -108 = -a - 105 ⇒ add 105 to both sides
∴ -3 = -a ⇒ multiply both sides by -1
∴ a = 3
- Substitute the value of a in the equation
∵ y = ax² + 2ax - 105
∴ y = 3x² + 2(3)x - 105
∴ y = 3x² + 6x - 105
- To find the x-intercept put y = 0
∴ 3x² + 6x - 105 = 0
- All the terms have 3 as a common factor
∴ divide all the terms by 3
∴ x² + 2x - 35 = 0
- Now factorize it into two factors
∵ x² = x × x ⇒ the 1st term in the bracket and the 1st term in the
2nd bracket
∵ -35 = -5 × 7 ⇒ the 2nd term in the 1st bracket and the 2nd term in the
2nd bracket
∵ x × - 5 = -5x ⇒ means
∵ x × 7 = 7x ⇒ extremes
∵ 7x - 5x = 2x ⇒ the middle term
∴ (x - 5)(x + 7) = 0
- Equate each bracket by 0
∴ x - 5 = 0 ⇒ add 5 to both sides
∴ x = 5
OR
∴ x + 7 = 0 ⇒ subtract 7 from both sides
∴ x = -7
∴ The x-intercept are -7 , 5
* The x-intercept are (-7 , 0) and (5 , 0)
Answer:
Step-by-step explanation:
Identify this conic section.
x2 - y2 = 16
o line
circle
ellipse
parabola
hyperbola
Answer:
hyperbola
Step-by-step explanation:
hyperbola
Ax^2+By^2+Cx+Dy+E=0
A=B you probably have a circle
A and B have same sign but A isn't B you probably have an ellipse
A and B are opposite in sign you probably have an hyperbola
If either A or B=0 (but not both) then you have a parabola
ANSWER
Hyperbola
EXPLANATION
The given conic has equation:
[tex] {x}^{2} - {y}^{2} = 16[/tex]
We divide through by 16.
[tex] \frac{ {x}^{2} }{16} - \frac{ {y}^{2} }{16} = \frac{16}{16} [/tex]
We simplify the right hand side to get
[tex] \frac{ {x}^{2} }{16} - \frac{ {y}^{2} }{16} = 1[/tex]
Or
[tex] \frac{ {x}^{2} }{ {4}^{2} } - \frac{ {y}^{2} }{ {4}^{2} } = 1[/tex]
This is a hyperbola, that has its vertex at the origin because the quadratic terms have different signs. One is positive and the other is negative.
20. –3 |z| + 2(a + y) what's the answer?
z=-4.2 a=-2 y=3
Answer:
-10.6
Step-by-step explanation:
-3|z| + 2(a + y) =
= -3|-4.2| + 2(-2 + 3)
= -3(4.2) + 2(1)
= -12.6 + 2
= -10.6
Review: To simplify an expression, combine like terms by adding or
subtracting coefficients only. Like terms have the same variable (letter or
symbol that represents a quantity).
Example: 17a + 4 - 5a - 3 = (17a - 5a) + (4-3) = 12a + 1
Simplify this expression. 10b + 7 - 3 - 2
Answer:
10b + 2
Step-by-step explanation:
To simplify this expression. 10b + 7 - 3 - 2 use the sample you demonstrated above to simplify it
10b + 7 -3 -2
combine the like terms
10b + 7 - 5
10b + 2
The expression 10b + 7 - 3 - 2, when simplified by grouping and adding or subtracting like terms, becomes 10b + 2.
Explanation:To simplify an expression, like the one you've given which is 10b + 7 - 3 - 2, it is necessary to group like terms and combine them.
First, let's combine like terms. In this case, you only have a single term with a variable:
10b (which we will leave as is since there are no other terms with 'b' in them)
Then, you have constants (numbers without variables) 7, -3, and -2. We can combine these by adding or subtracting them: 7 - 3 - 2 = 2
So your simplified expression becomes: 10b + 2
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HELP Geometry does anyone know this
Answer: second option.
Step-by-step explanation:
You need to remember the following identity:
[tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]
In this case, we can observe that:
[tex]\alpha=45\°\\opposite=6\\hypotenuse=x[/tex]
Now you must substitute these values into [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex] and solve for the hypotenuse. Then:
[tex]sin(45\°)=\frac{6}{x}\\\\(x)(sin(45\°))=6\\\\x=\frac{6}{sin(45\°)}\\\\x=6\sqrt{2}[/tex]
Answer:
The correct answer is second option
6√2
Step-by-step explanation:
From the figure we can see a right angled triangle, with angles 45°, 45° and 90°
The height of triangle is 6 units
Points to remember
If the angles of a right angled triangle are 45°, 45° and 90° then the sides are in the ratio, 1 : 1 : √2
To find the value of x
From the figure we can see that, the angles are 45°, 45° and 90°
Therefore the two sides are equal and one side is x
The equal side is 6 units
Therefore 6 : 6 : x = 6 : 6 : 6√2
The value of x = 6√2
The second option is the correct answer.
Help pls !!! A waitress kept track of whether her customers ordered and appetizer and dessert
The 0.3 in the highlighted cell mean 30% ordered dessert but no appetizer.
The correct option is (D).
What is mean?The mean (aka the arithmetic mean, different from the geometric mean) of a dataset is the sum of all values divided by the total number of values.
As, the number is in the column with no appetizer and row with dessert
So, 0.3 = 0.3*100/100
= 30/100
= 30% ordered dessert but no appetizer.
Hence, 30% ordered dessert but no appetizer.
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What is the area of the triangle formed from (-2,2), (1,2), and (0,-6)?
A.12 square units
B.48 square units
C.8 square units
D.24 square units
Answer:
Option A.12 square units
Step-by-step explanation:
Let
[tex]A(-2,2), B(1,2), C(0,-6)[/tex]
Plot the vertices
see the attached figure
we know that
The area of triangle is equal to
[tex]A=\frac{1}{2}(b)(h)[/tex]
where
[tex]b=AB=(1-(-2))=3\ units[/tex]
[tex]h=(2-(-6))=8\ units[/tex]
substitute
[tex]A=\frac{1}{2}(3)(8)[/tex]
[tex]A=12\ units^{2}[/tex]
Answer:
Step-by-step explanation:
A. 12
Please help! Evaluate 1 + ( - 2/3 ) - (-m) where m - 9/2.
Answer:
[tex]m + \frac{1}{3} [/tex]
Step-by-step explanation:
[tex]1. \: 1 - \frac{2}{3}+m \\ 2. \: m + (1 - \frac{2}{3}) \\ m + \frac{1}{3} [/tex]
Answer:
29/6
Step-by-step explanation:
1+ -2/3 - (-m)
1 - 2/3 + m
1/3 + m
Let m = 9/2
1/3 +9/2
Get a common denominator of 6
1/3 *2/2 = 2/6
9/2 *3/3 = 27/6
2/6 + 27/6
29/6
What is the equation of the line passing through the points (-25,50) and (25,50 in slope intercept form?
Answer:
y=50
Step-by-step explanation:
Since the y value doesn't change and it is a line
y=50
Answer:
[tex]y= 0x + 50[/tex]
Step-by-step explanation:
Since, the slope intercept form of a line is,
y = mx + c,
Where, m is the slope of the line.
Also, the equation of a line passes through [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Thus, the equation of the line passes through (-25, 50) and (25, 50) is,
[tex]y-50= \frac{50-50}{25+25}(x+25)[/tex]
[tex]y-50=0[/tex]
[tex]\implies y = 0x + 50[/tex]
Which is the required equation.
Can someone help me plz
Answer:
Half gallon
Step-by-step explanation:
at the least expensive price per ounce (60 cents), half gallon is the answer.
5 1/8 - 2/ 78 my little sister's homework
Answer:
5 1/8 - 2 7/8 =
3 -6/8 =
2 2/8 =
2 1/4 =
2.25
Step-by-step explanation:
given sin(0)= -1 and cos(0)= 0, what is the angle measurement of 0 in radians
Check the picture below.
The nth term of a sequence is n^2 + 20.
a) work out the first three terms of the sequence
b) how many terms in the sequence are less than 50?
Answer:
[tex]\large\boxed{a)\ 21,\ 24,\ 29}\\\boxed{b)\ \text{five terms}}[/tex]
Step-by-step explanation:
[tex]a_n=n^2+20\\\\a)\\\\\text{Substitute}\ n=1,\ n=2\ \text{and}\ n=3\ \text{to the }\ a_n:\\\\a_1=1^2+20=1+20=21\\\\a_2=2^2+20=4+20=24\\\\a_3=3^2+20=9+20=29[/tex]
[tex]b)\\\\\text{You have to solve the inequality:}\\\\n^2+20<50\qquad\text{subtract 20 from both sides}\\\\n^2<30\to n<\sqrt{30}\to n\leq5\\\\a_1,\ a_2,\ a_3,\ a_4\ \text{and}\ a_5\ \text{are less than 50.}[/tex]
a) The first three terms of the sequence are 21, 24 and 29.
b) The no. of terms less than 50 are 6.
What are arithmetic and geometric sequence?An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference
d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.
In a geometric sequence numbers are written in the same constant ratio(r).
It means every next number is a multiple of a common constant and the previous number.
r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.
Given, The nth term of a sequence is n² + 20.
The first three terms we'll get by replacing 1, 2, and 3 in place of n.
The first term is (1)² + 20 = 21.
The second term is (2)² + 20 = 24.
The third term is (3)² + 20 = 29.
No. of terms that are less than 50 are
n² + 20 < 50.
n² < 30.
n < ± √30.
n < 6 approx.
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A system of equations is shown below. Which ordered pair represents the solution to the system
Answer:
The correct answer is (-5,-5)
Step-by-step explanation:
1. Both of the equations are in standard form, so first you set them equal to each other.
2. Solve for x as a normal algebraic equation.
3. Back substitute your answer for x into one of the original equations. (back substitution is just putting the x back into the equation and solving for y.)
4. Now you have your x and y coordinates, and the point of intersection of the two lines.
The ordered pair represents the solution to the system is (-5, -5), and the correct option is A.
What is the ordered pair?A pair of numbers that are written in a particular order, enclosed in brackets are known as ordered pairs.
The given system of equation is;
y = 3x + 10
y = 5x +20
Subtraction equation 1 from 2
y - y = 3x + 10 - 5x -20
0 = -2x -10
2x = -10
x = -10/2
x = -5
Substitute the value of x in equation 1
y = 3x + 10
y = 3(-5) +10
y = -15 +10
y = -5
Hence, the ordered pair represents the solution to the system is (-5, -5), and the correct option is A.
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What is the length of AB?
A(2,-6). BIZ, 1)
Answer:
The length of AB is [tex]\sqrt{74}\ units[/tex]
Step-by-step explanation:
we know that
The formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
[tex]A(2,-6)\\B(7,1)[/tex]
substitute
[tex]d=\sqrt{(1+6)^{2}+(7-2)^{2}}[/tex]
[tex]d=\sqrt{(7)^{2}+(5)^{2}}[/tex]
[tex]d=\sqrt{49+25}[/tex]
[tex]AB=\sqrt{74}\ units[/tex]
The table shows the number of candies packed by machine c. the equation shows the number of candies packed by machine D. In both representations, x is a measure of the number of minutes and y is a measure of the number of candies packed. How many more candies could machine d pack than machine c in 11 minutes
Answer: 605 candies
Step-by-step explanation:
Machine C shows a table where 150 candies are added every 2 minutes (which equals 75 candies per minute). Extend the table to show how many candies are made in 11 minutes:
x y
(minutes) (candies)
2 150
4 300
6 450
8 600
10 750
11 825
Machine D productivity is given by the equation y = 130x
when x = 11 minutes, y = 130(11)
= 1430 candies
The difference between machines C and D is: 1430 - 825 = 605
What is the solution to the compound
2/2 - 7x-4
Simplify
- 58+4
2x + 1
2-1
2x + 1
*+1
2-72
Answer:
A or (2x+1)/(x-1)
Step-by-step explanation:
Let's simplify the top of the fraction first.
1. Simplify the numerator.
2x^2 -7x-4=(2x+1)(x-4)
2. Simplify the denominator.
x^2-5x+4=(x-4)(x-1)
Now we have:
((2x+1)(x-4))/((x-4)(x-1))
We see that there is an (x-4) both on the numerator and denominator.
We can remove (x-4) by division.
Doing that, we have:
(2x+1)/(x-1) or A
translate the following situation into an inequality statement . Lily has $25 to spend on a charm bracelet for her sisters birthday gift the cost of the bracelet is $12 plus $1.50 per charm
Final answer:
Lily's budget scenario with her sister's charm bracelet is translated into the inequality statement 12 + 1.50c ≤ 25, where c represents the number of charms she can buy. Solving this inequality will show how many charms Lily can afford without exceeding her $25 budget.
Explanation:
The question involves translating a real-life situation into an inequality statement concerning budget and expenses. Lily has $25 to spend on her sister's birthday gift, which is a charm bracelet. The cost structure for the bracelet is $12 for the bracelet itself plus $1.50 for each charm. We let the number of charms she plans to buy be represented by c. The total cost for these charms would be $1.50c, and when added to the initial $12 for the bracelet, the sum should not exceed Lily's budget of $25.
Therefore, the inequality that represents this situation is 12 + 1.50c ≤ 25.
To find the maximum number of charms Lily can afford, we would solve for c in the inequality. This step involves subtracting 12 from both sides and then dividing by 1.50.
What is the factored form of 8x2 + 12x?
Answer:
[tex]4x(2x + 3)[/tex]
Step-by-step explanation:
We have the expression
[tex]8x^2 + 12x[/tex]
and we must factor it
Note that the expression has no independent term
Then we can factor the expression by taking the variable 4x as a common factor
[tex]8x^2 + 12x[/tex]
[tex]4x(2x + 3)[/tex]
Finally the factored form of [tex]8x^2 + 12x[/tex] is [tex]4x(2x + 3)[/tex]
Answer: 4x(2x+3).
Step-by-step explanation: To factor a number means to break it up into numbers that can be multiplied together to get the original number. In the given problem, we can factorize the expression by taking out a common factor, in this case 4x:
[tex]8x^{2} +12x=[/tex]
[tex]4x(2x+3)[/tex]
as we can see, if we multiply 4x*(2x+3) we obtain the original expression.
What is the total surface area of this square pyramid?
Answer:
S.A. = 297 mm²Step-by-step explanation:
We have a square in the base and four triangles on the lateral surface.
The formula of an area of a square:
[tex]A_{\square}=s^2[/tex]
s - side
We have s = 9mm. Susbtitute:
[tex]A_{\square}=9^2=81\ mm^2[/tex]
The formula of an area of a triangle:
[tex]A_{\triangle}=\dfrac{bh}{2}[/tex]
b - base
h - height
We have b = 9 mm and h = 12 mm. Substitute:
[tex]A_{\triangle}=\dfrac{(9)(12)}{2}=54\ mm^2[/tex]
The Surface Area:
[tex]S.A.=A_{\square}+4A_{\triangle}[/tex]
Substitute:
[tex]S.A.=81+4(54)=297\ mm^2[/tex]
Answer:
278
Step-by-step explanation:
what are the soultion(s) to the quadratic equation 40- x^2=0
Answer:
40 - x² = 0
x² = 40
x = ±√40 = ±√4√10 = ±2√10
Ava wants to figure out the average speed she is driving. She starts checking her car’s clock at mile marker 0. It takes her 4 minutes to reach mile marker 3. When she reaches mile marker 6, she notes that 8 minutes total have passed since mile marker 0.
What is the average speed of the car in miles per minute?
mile(s) per minute
What is an equation of the line that represents n, the number of mile marker passed, as a function of t, time in minutes?
Answer:
0.75 and n-6= 0.75(t-8)
Step-by-step explanation:
To find the average speed of Ava's car, divide the total distance traveled by the total time taken. Ava travels 6 miles in 8 minutes, so the average speed is 0.75 miles per minute. The equation of the line representing the number of mile markers passed as a function of time is n = (3/4)t.
Explanation:To find the average speed of Ava's car in miles per minute, we can use the formula:
Average speed = total distance / total time
First, we need to find the total distance traveled. Ava travels from mile marker 0 to mile marker 6, which is a distance of 6 miles.
Next, we need to find the total time it took Ava to travel this distance. Ava notes that 8 minutes have passed when she reaches mile marker 6, but it took her 4 minutes to travel from mile marker 0 to mile marker 3. This means it took her 4 minutes to travel 3 miles. Therefore, it would take her an additional 4 minutes to travel the remaining 3 miles from mile marker 3 to mile marker 6.
So, the total time taken by Ava to travel 6 miles is 4 minutes + 4 minutes = 8 minutes.
Now, we can use the formula to calculate the average speed:
Average speed = total distance / total time = 6 miles / 8 minutes = 0.75 miles per minute.
Equation of the line:
To find the equation of the line that represents the number of mile markers passed as a function of time, we can use the equation:
n = mt + b
Here, 'n' represents the number of mile markers passed, 't' represents time in minutes, 'm' represents the slope of the line, and 'b' represents the y-intercept.
In this scenario, Ava starts checking her car's clock at mile marker 0, which means the y-intercept is 0. We also know that Ava takes 4 minutes to travel from mile marker 0 to mile marker 3, which means she passes 3 mile markers in 4 minutes. Therefore, the slope of the line is 3/4.
So, the equation of the line is: n = (3/4)t.
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Answer ASAP!!It takes 1 1/2 cups of flour, cups of sugar, and 1 1/4 cup of butter to bake fifteen shortbread cookies. If Ramon has 5 cups of flour, 4 cups of sugar, and 13/4 cups of butter, how many shortbread cookies can he bake? Plz don't copy and paste the answer from another site. I need it to be answered in fraction form and well explained. Brainliest for first correct!
Answer:
Up to 39 shortbread cookies.
Step-by-step explanation:
Start by considering: how many cookies can Ramon make if
Flouring runs out first,Sugar runs out first, and Butter runs out first?Assume that flour runs out before the other two ingredients. How many cookies can Ramon make?
It takes 1 1/2 = 3/2 cups of flour to bake fifteen cookies. 5 cups of flour is available. How many batches of fifteen cookies will that 5 cups of flour make?
[tex]\displaystyle \frac{5}{3/2}\right = \frac{10}{3}[/tex].
That's
[tex]\displaystyle 5\times \frac{10}{3} = 50\;\text{cookies}[/tex].
Similarly, assume that sugar runs out before the other two ingredients. How many cookies can Ramon make?
It takes one cup of sugar to bake fifteen cookies. 4 cups of sugar is available. That 4 cups of sugar will make up to four batches of fifteen cookies. That's 60 cookies.
Assume that butter runs out before the other two ingredient. How many cookies can Ramon make?
It takes 1 1/4 = 5/4 cups of butter to bake fifteen cookies. 13/4 cups of butter is available. That 13/4 cups of butter will make up to 13/5 batches of fifteen cookies. That's
[tex]\displaystyle 15 \times \frac{13}{5} = 39\;\text{cookies}[/tex].
These three numbers differ. How many cookies will these materials actually make? The ingredient that will make the smallest number of cookies will run out before other ingredients. In this case, butter runs out first. These materials will make up to 39 shortbread cookies.