If you compare the functions:
[tex]\begin{gathered} f(x)=4x+9 \\ g(x)=4x+7 \end{gathered}[/tex]Considering f(x) as the parent function, let's analyze each option:
1) Translation 2 units right.
To translate a function 2 units to the right, you have to subtract 2 to the x-term:
[tex]\begin{gathered} h(x)=f(x-2)=4(x-2)+9 \\ h(x)=4\cdot x-4\cdot2+9 \\ h(x)=4x-8+9 \\ h(x)=4x+1 \end{gathered}[/tex]As you can see the resulting function, h(x), is not equal to g(x), which means that the transformation applied was not a shift 2 units to the right.
2) Translation 2 units to the left
To translate the function two units to the left, you have to add 2 to the x-term:
[tex]\begin{gathered} i(x)=f(x+2)=4(x+2)+9 \\ i(x)=4\cdot x+4\cdot2+9 \\ i(x)=4x+8+9 \\ i(x)=4x+17 \end{gathered}[/tex]The resulting function, i(x), is not equal to g(x), which means that the transformation applied was not a shift of 2 units to the left.
3) Translation 2 units up
To translate a function 2 units up, you have to add 2 to the function, that is:
[tex]\begin{gathered} j(x)=f(x)+2=(4x+9)+2 \\ j(x)=4x+9+2 \\ j(x)=4x+11 \end{gathered}[/tex]The function j(x) is different from the function g(x), so the transformation applied was not a shift 2 units up.
4) Translation 2 units down
To shift a function two units down, you have to subtract 2 from the function:
[tex]\begin{gathered} k(x)=f(x)-2 \\ k(x)=(4x+9)-2 \\ k(x)=4x+9-2 \\ k(x)=4x+7 \end{gathered}[/tex]The functions k(x) and g(x) are equal, which means that to determine the function g(x) the function f(x) was translated 2 units down.
Answer:
1,3,4
Step-by-step explanation:
keep it easy
George has a triangle-shaped garden in his backyard. He drew a model of this garden on a coordinate grid with vertices A(4, 2), B(2, 4), and C(6, 4). He wants to create another, similar-shaped garden, A'B'C', by dilating triangle ABC by a scale factor of 0.5. What are the coordinates of triangle A'B'C'? A. A'(2, 2), B(1, 2). C'(3, 2) B. A'(2, 1), B(1, 2). C'(3, 2) C. A'(8,4), B'(4, 8), C'(12, 8) D. A(2, 1), B(1, 2), C'(6, 4)
Hello, we have drawn the triangular region indicated in the first photo and we will find the side lengths of the triangle by means of the right triangles you see in red and green. (Using the Pythagorean Theorem) The triangular region indicated represents an isosceles triangle. Its base is [tex]4[/tex] units.
Next, we take half the length of the sides. Draw a triangle with base [tex]2[/tex] units and each of its lateral sides with [tex]\sqrt{2}[/tex] units.
Only Option B meets this condition. I wish you success.
Three sisters share some money. the oldest gets 5/11 of the share. The older gets 7/12 of the remainder. what fraction of the money does the old girl gets?
The fraction of the money the old girl gets is 7x/22 and the oldest gets 5x/11.
How much does an older girl get?Given,
Oldest gets 5/11 of the share.
The older gets 7/12 of the remainder.
Solution:
Let x be the total amount.
Oldest share = 5/11*x
= 5x/11
Older share =( x - 5/11*x)*7/12
= (11x-5x/11)*7/12
= 6x/11*7/12
= 42x/132
= 21x/66
=7x/22
The fraction of the money the old girl gets is 7x/22 and the oldest gets 5x/11.
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can someone please help me !!!!!!!!!!!!!!!!!!!!!!!!11
answer
: I think it's -70 I'm not 100 percent sure but I think
Answer:
m is undefind
Step-by-step explanation:
sorry for the scribbles i got confused
m=m
Hi help with this please
(03.05)
Given f(x) and g(x) = f(x) + k, look at the graph below and determine the value of k. (1 point)
k=
Pic Below
Given f(x) and g(x) = f(x) + k, from the graph, we can determine the value of k as 4 units.
In the question,
Given f(x) and g(x) = f(x) + k
From the graph, we can say that there is a shift of 4 units up between f(x) and g(x).
The given lines are parallel lines, so their slopes will be the equal but intercepts will be different for both the lines.
The y-intercept of f(x) = -3 and that of g(x) = 1
Hence, the difference between the intercepts when calculated is (1 -(-3)) = 4.
Therefore, g(x) = f(x) + 4
So, the value of k is 4.
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Solve the simultaneous equations.
x^2+y^2=13
y=x+1
Solving the simultaneous equation gives x as 2 and y as 3
How to solve the simultaneous equationFrom the information given, we have the equations as;
x² + y² = 13 equation (1)y = x + 1 equation (2)Now, substitute the value of y as x + 1 in equation (2) into the equation (1)
We have;
x² + (x + 1)² = 13
expand the bracket
x² + (x + 1)(x+1) = 13
x² + x² + x + x +1 = 13
collect like terms
2x² + 2x + 1 - 13 = 0
2x² + 2x - 12 = 0
Factorize the equation
2x² + 6x - 4x - 12 = 0
Factor the common terms
2x(x + 3) - 4(x + 3) = 0
2x - 4 = 0
x = 2
x = -3
Substitute x as 2 into equation (2)
y = x + 1
y = 2 + 1
y = 3
Hence, the values are 2 and 3
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(-1, 1) (1, -1) (2, -2) (-2, 2) (1, -2) is it a function?? how do I explain if it is? please help! thanks :)
Answer:
This relation is NOT a function
Step-by-step explanation:
As you see in the attached image, the x value of 1 has 2 different points assigned to it. This relation would fail the vertical line test, therefore it is not a function.
Key words:
Relation: Any graph
Function: A relation that has 1 y value for every x value
Vertical line test: An imaginary line drawn on a relation/function to test if it is a function. (in some cases, like this relation, you will see right away from the placement of the points that it is not a function)
Hope that helps
Ben sells greeting cards for $5 each in his online store. He also charges $1.99 for shipping. The total
cost, y, of an order from Ben’s store is found using the equation y = 5x + 1.99, where x is the number of
cards bought. Which quantity represents the dependent variable in this problem situation?
The quantity which represents the dependent variable in this problem situation is: A. the number of cards sold.
The types of variables.In Mathematics, there are two (2) main types of variables and these include the following:
Dependent variable.Independent variable.What is a dependent variable?A dependent variable can be defined as the variable which signifies the effect of an independent variable and it is dependent on other factors because it's the part of an experiment that's being observed or measured.
Based on the information provided in this scenario, we can reasonably infer and logically deduce that the dependent variable is the number of greeting cards sold by Ben.
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Complete Question:
Ben sells greeting cards for $5 each in his online store. He also charges $1.99 for shipping. The total cost, y, of an order from Ben’s store is found using the equation y = 5x + 1.99, where x is the number of cards bought. Which quantity represents the dependent variable in this problem situation?
A. the number of cards sold
B. the total cost of an order
C. the cost of one card
What’s the answer plss
Answer:
∠M
Step-by-step explanation:
∠M is the only vertex that does not already have an indicated angle. There are three vertexes, being 90° at ∠K (the box-like figure means it is a right angle, therefore 90°) , 61° at ∠N , and ∠M, which does not have a given angle.
Find the midpoint between coordinates (-8,6)
and (-10,4)
Answer:
(-9, 5)
Step-by-step explanation:
A midpoint is the point, or center at the middle of two given points.
The midpoint formula:
[tex](Xm, Ym)= (\frac{x1 + x2}{2}), (\frac{y1 + y2}{2})[/tex]
X1, Y1 is an endpoint
X2, Y2 is an endpoint.
Explanation:
X1, Y1= (-8, 6)
X2, Y2= (-10, 4)
[tex]Xm, Ym= \frac{(-8)+(-10)}{2}, \frac{(6+(4)}{2}[/tex]
[tex]Xm, Ym= \frac{-18}{2}. \frac{10}{2} \\\\Xm, Ym= (-9, 5)[/tex]
The Midpoint is (-9, 5)
What is the prime factorization of 175?
Answer: 5 x 5 x 7
Step-by-step explanation: 5 x 5 x 7
In Exponential Form:
52 x 71
CSV Format:
5, 5, 7
Prime[3] = 5, Prime[4] = 7
Focus (5, 6) and Directrix x = 1
Answer:
kitchen scaleuwueieie
A bag contains 80 more red marbles than black marbles. Ifthe ratio of red marbles 9 to 4, how many marbles are in the bag in total?
The ratio of red marbles to black marbles is 9:4, this implies:
[tex]\frac{x+80}{x}=\frac{9}{4}[/tex]By cross-multiplying and solving for x, we have:
[tex]\begin{gathered} 9x=4(x+80) \\ 9x=4x+320 \\ 9x-4x=320 \\ 5x=320 \\ x=\frac{320}{5} \\ x=64 \end{gathered}[/tex]Thus, the number of red marbles is 64+80=144 and the number of black marbles is 64.
Hence, the total number of marbles in the bag is:
[tex]144+64=208\text{ marbles}[/tex]A student believes there is a correlation between the number of texts sent during class and gpa. the student collected data and found that the line of fit can be modeled by the equation ŷ = 3.9 − 0.1x. identify and interpret the slope in this scenario. the slope is 3.9. starting at 0.1, the gpa will increase by 3.9 for every text sent in class. the slope is 3.9. starting at 0.1, the gp will decrease by 3.9 for every text sent in class. the slope is −0.1. starting at 3.9, the gpa will increase by 0.1 for every text sent in class. the slope is −0.1. starting at 3.9, the gpa will decrease by 0.1 for every text sent in class.
The slope is -0.1 starting at 3.9, the GPA will decrease by 0.1 for each text sent in class.
Here we have to find the slope.
The equation given is:
y = 3.9 - 0.1x
As we know that the equation of a line is:
y = mx + c
Therefore we get that the slope is m = -0.1
Starting at 3.9 the GPA will decrease by 0.1 for every text sent in class ( for y = mx + b, a is the slope which is the coefficient of x)
Because the slope is less than 0, it is decreasing.
Therefore the slope is -0.1 and there is a decrease in GPA of 0.1.
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i dont know the answer ..can i get help?
I need help I have to trun it in I have like 5 minutes
Simplifying the given expression, the passcode would be: CDOPWR.
How to Simplify an Expression?To simplify an expression means to solve to find the value in its simplest form.
Simplify the given expression as explained below:
P. 1/2 + 2/3 - 4.25
= 1.17 + 4.25 [addition]
= 5.42
R. -7 * -4 + 3.5
28 + 3.5 [multiply before adding based on PEMDAS]
= 31.5
D. -5.6 + 2.7 - 3.2 = -6.1
W. 3/4 - 0.25 + 6.8
0.75 - 0.25 + 6.8 = 7.3 [apply PEMDAS]
C. -2 * 4.3 - 7.1 [apply PEMDAS]
= -8.6 - 7.1
= -15.7
O. 1/2 + 0.5 - 2/5 [convert all fractions to decimals]
0.5 + 0.5 - 0.4 = 0.6
From the least to the greatest, the passcode would be: CDOPWR.
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Grab the image of kite EFGH after of a reflection over the line y=1
Please help I’m literally about to cry
Check the picture below.
After plotting the data where x-the side of a polygon, and f(x)= the area of the polygon, Jack used technology and determined the appropriate model to approximate the area of the polygon, F(x)=x² + 3x + 2. Use the model Jack created to predict the area of a polygon that has a side length of 3.
19 18 20 10
Answer: The answer would be D. 20 Because u plug 3 in for x so F(x)= 9+9+2
Step-by-step explanation:
True or False:
The Commutative Property of Multiplication states that for all expressions a and b, ab = ba.
How do I solve this problem 2 5/12 = 3 1/4 + k
Answer:
Step-by-step explFirst, convert each mixed number into an improper fraction:
2
5
12
=
−
3
1
4
+
k
2
+
5
12
=
−
(
3
+
1
4
)
+
k
(
12
12
×
2
)
+
5
12
=
−
(
[
4
4
×
3
]
+
1
4
)
+
k
24
12
+
5
12
=
−
(
12
4
+
1
4
)
+
k
29
12
=
−
13
4
+
k
Next, add
13
4
to each side of the equation to isolate
k
while keeping the equation balanced:
13
4
+
29
12
=
13
4
−
13
4
+
k
13
4
+
29
12
=
0
+
k
13
4
+
29
12
=
k
Then, we need to put
13
4
over a common denominator so we can add the two fractions by multiplying it by an appropriate form of
1
:
(
3
3
×
13
4
)
+
29
12
=
k
39
12
+
29
12
=
k
68
12
=
k
Now, if necessary we can convert the improper fraction back into a mixed number:
60
12
+
8
12
=
k
5
+
4
×
2
4
×
3
=
k
5
+
4
×
2
4
×
3
=
k
5
+
2
3
=
k
5
2
3
=
k
k
=
5
2
3
NEED ANSWER ASAP
any answers are appreciated
part a. use the diagram to write an equation and solve for x. show your work
part b. use your answer from part a for x, and find the measure of both angles. select two answers
- 116
- 68
- 61
- 112
- 119
- 64
Answer:
×= 38
2x-15 = 61°
3×+5= 119°
Step-by-step explanation:
2×-15+3x +5= 180
180+10= 190
190 ÷5x
×=38
Answer:
a) x = 38
b) 61° and 119°
Step-by-step explanation:
Same-side Exterior Angles Theorem
When two parallel lines are intersected by a transversal, the angles that are exterior to the parallel lines and on the same side of the transversal line are supplementary (sum to 180°).
Part (a)Using the Same-side Exterior Angles Theorem, equate the sum of the two angles to 180° and solve for x:
⇒ (2x - 15)° + (3x + 5)° = 180°
⇒ 2x - 15 + 3x + 5 = 180
⇒ 5x - 10 = 180
⇒ 5x = 190
⇒ x = 38
Part (b)Substitute the found value of x from part (a) into the expressions for each angle:
⇒ (2x - 15)°
⇒ (2(38) - 15)°
⇒ (76 - 15)°
⇒ 61°
⇒ (3x + 5)°
⇒ (3(38) + 5)°
⇒ (114 + 5)°
⇒ 119°
Therefore, the two angles are 61° and 119°.
write an equivalent expression to (x + 2) + 5y
Answer:
5y + x + 2 is one.
Step-by-step explanation:
Another one: x + (2 + 5y)
Solve for x
1.5x = 25+x
Answer:
x = 50
Step-by-step explanation:
in pic
please help!
The Equation P= 2.5m + 35 represents the price P (in dollars) of a bracelet, where m is the cost of the materials (in dollars). The price of a bracelet is $115. What is the cost of the materials?
Answer:
The cost of materials is $32.
Step-by-step explanation:
You can solve this in a simple manner:
115 = 2.5m + 35
115-35 = 2.5m
80 = 2.5m
m = 32
You can check your answer by putting 32 back into the equation(P=2.5m+35) and you should get 115(which is price of bracelet)
help please please please
Answer:
Step-by-step explanation:
-1 + 14x = 12x + 17
-12x -12x
-1 + 2x = 17
+1 +1
2x = 18
x is equal to 9
hope this helps!
Kate's middle school graduation party will be at the skating rink. The cost for each person is $15. The cost of the room for the party's $80 katies parents have set a budget of $478.
Given the function 15z +80=470, determine the maximum number of people who can be at the party.
Answer:
26 people
Step-by-step explanation:
15z +80 = 478
15z = total cost of the people
80 = cost of room
478 = budget
15z + 80 = 478
Subtract 80 from both sides
15z = 398
z = 26.53333
You can't have a decimal person
z = 26
Hope this helps :)
Have a nice day
does anyone know how to graph trigonometric functions for algebra 2?
Solution:
Give the following below
[tex]\begin{gathered} amplitude=3 \\ period=\frac{\pi}{2} \\ midline,\text{ }y=-1 \\ Passing\text{ through the point }(0,2) \end{gathered}[/tex]To find the cosine function, we will apply the general formula for cosine function below
[tex]\begin{gathered} f(x)=a\cos(bx-c)+d \\ Where \\ a\text{ is the amplitude} \\ b\text{ represents the speed of the cycle} \\ d\text{ is the vertical shift} \\ \frac{c}{b}\text{ is the phase shift \lparen horizontal shift\rparen} \\ Period=\frac{2\pi}{b} \end{gathered}[/tex]To find the value of b
[tex]\begin{gathered} Period=\frac{\pi}{2} \\ \frac{2\pi}{b}=\frac{\pi}{2} \\ Crossmultiply \\ b\times\pi=2\times2\pi \\ b=\frac{4\pi}{\pi} \\ b=4 \end{gathered}[/tex][tex]\begin{gathered} a=3 \\ b=4 \\ d=-1 \\ c=0 \end{gathered}[/tex]Substitute the values of the variables into the general formula for cosine function
[tex]\begin{gathered} f(x)=a\cos(bx-c)+d \\ f(x)=3\cos(4x-0)-1 \\ f(x)=3\cos4x-1 \end{gathered}[/tex]Applying a graphing tool,
The graph of one cycle of the function is shown below
Sydney is 5 feet and 1 inch tall. What would her height be in centimeters? (1 foot = 12 inches, 1 inch = 2.54 centimeters
Eli has a points card for a movie theater.
• He receives 40 rewards points just for signing up.
• He earns 7.5 points for each visit to the movie theater.
• He needs 100 points for a free movie ticket.
How many visits must Eli make to earn a free movie ticket?
Answer:
8 visits
Step-by-step explanation:
x=# of visits
100=40+7.5x
60=7.5x
x=8
hope this helps :)
Answer:
A
tyler has a points card for a movie theater.
he receives 75 rewards points just for signing up.
• he earns 10.5 points for each visit to the movie theater.
he needs 180 points for a free movie ticket.
.
a
how many visits must tyler make to earn a free movie ticket?
Step-by-step explanation: hqwediywydgwq78d
PLEASE HELP!!!
Josie is participating in a charity bike ride. This table and graph represent her performance during the ride where x is the number of hours Josie rides and y is her distance from the finish line. Match the quantity to the correct feature and interpretation.
Hours (x) 0 2 4 6 Kilometers away from finish line (y) 75 50 25 0
(ur answer) The x-intercept. The amount of time, in hours, that has passed when Josie completes the race.
(ur answer) The y-intercept. Josie's distance, in kilometers, from the finish line when she begins the ride.
(ur answer) The slope: the absolute value of the slope represents the speed Josie is riding in kilometers per hour.
ANSWERS TO PUT IN:
1. -25/2
2. 6
3. 75
The value of the x-intercept is 6, the y-intercept is 75, and the value of the slope is -25/2.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The x-intercept from the graph(where y = 0)
The x-intercept = 6
The y-intercept from the graph(where x = 0)
The y-intercept = 75
The slope can be found using two points: (0, 75) and (2, 50)
[tex]\rm m =\dfrac{50-75}{2-0}[/tex]
m = -25/2
Thus, the value of the x-intercept is 6, the y-intercept is 75, and the value of the slope is -25/2.
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