Given:
A student says that the graph of the equation [tex]y = 3(x + 8)[/tex] is the same as the graph of [tex]y = 3x[/tex], only translated upwards by 8 units.
To find:
Whether the student is correct or not.
Solution:
Initial equation is
[tex]y=3x[/tex]
[tex]f(x)=3x[/tex]
Equation of after transformation is
[tex]y=3(x+8)[/tex]
[tex]g(x)=3(x+8)[/tex]
Now,
[tex]g(x)=f(x+8)[/tex] ...(i)
The translation is defined as
[tex]g(x)=f(x+a)+b[/tex] ...(ii)
Where, a is horizontal shift and b is vertical shift.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
From (i) and (ii), we get
[tex]a=8\text{ and }b=0[/tex]
Therefore, the graph of [tex]y=3x[/tex] translated left by 8 units. Hence, the student is wrong.
(-1,1) and (0,4) are on the line what is the linear equation in standard form
Answer:
y-3x=4
Step-by-step explanation:
1-4/-1-0=3
1 = 3(-1)+b
1=-3+b
b=4
The equation of linear equation in standard form consisting points (-1, 1) and (0, 4) is,
⇒ y = 3x + 4
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (-1, 1) and (0, 4)
Now,
Since, The equation of line passes through the points (-1, 1) and (0, 4).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (4 - 1) / (0 - (-1))
m = 3 / 1
m = 3
Thus, The equation of line with slope 3 is,
⇒ y - 1 = 3 (x - (-1))
⇒ y - 1 = 3 (x + 1)
⇒ y - 1 = 3x + 3
⇒ y = 3x + 3 + 1
⇒ y = 3x + 4
Therefore, The equation of linear equation in standard form is,
⇒ y = 3x + 4
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If DE=2x-1, what is the value of x
1. 7
2. 7.5
3. 8
4. 8.5
The value of the variable 'x' will be 8.5. Then the correct option is D.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
In the diagram below, ΔABC with sides of 13, 15, and 16, is mapped onto ΔDEF after a clockwise rotation of 90°.
The side AB is equal to DE. Then we have
DE = AB
2x - 1 = 16
2x = 16 + 1
2x = 17
x = 17/2
x = 8.5
The value of the variable 'x' will be 8.5. Then the correct option is D.
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Please help I’m stuck on this one!
Answer: The length of JK is 10.5 m
Step-by-step explanation:
Find the circumference C= dπ
C = 12π
C= 37.7
There are 360 degrees in a circle's circumference, so you can find the length of the arc by using the ratio of the arc to the whole circumference.
Multiply the Circumference by 100/360 (or 5/18 × 37.7)
The arc is 10.5 m
HELP 1 QUESTION.... Write a plan for proving that <1 is congruent to <2
Answer:
corresponding angles
Alternate angle
cointerior angle
Mira has breakfast at a restaurant. She leaves a 20\%20%20, percent tip of \$1.80$1.80dollar
Answer:
Price of Mira Breakfast = 9 $ before tip
Step-by-step explanation:
Let say Mira's breakfast Price = B $
Tip she left = 20 %
20 % Tip amount = (20/100) B = 0.2B $
Tip Amount She left = $ 1.8
Equating Tip Amount
0.2B = 1.8
=> B = 9
Price of Mira Breakfast = 9 $ before tip
Step-by-step explanation:
can someone pls help Write the following equation as a sentence: w = (15)(165)
Answer:
width equals fifteen times one hundred sixty five
is that right or is that ok or good enough?? sorry if i am wrong....
Answer:
W = 2475
Step-by-step explanation:
I am not sure if you want the answer or not but I hope this helps
3. x + y = 15
X - y = 3
solving systems of equations
Answer: x=10 y=5 = 15xy
Step-by-step explanation:
PLEASE HElP BEfORe MY BRAIN StarTs LagGiNg
Answer:
A.
Step-by-step explanation:
your equation has no exponents, it is linear.
Answer:
A
Step-by-step explanation:
3. Choose the correct statement below:
a) All natural numbers are whole numbers.
b) All whole numbers are natural numbers.
someone please help !!!
Fond the product of 2x4(2x+3x+4)
Answer:
10x⁵ + 8x⁴
Step-by-step explanation:
What is the difference between an image under a dilation with a scale factor 0 1
Kyra walks 2 miles in 30 minutes, how long will it take her to walk 120 minutes.
Answer:
if she walks 2 miles in 30 minutes, she will walk 8 miles in 120 minutes.
Step-by-step explanation:
Can i get brainliest plzzz?
Answer:
8
Step-by-step explanation:
They can walk 8 miles in 120 minutes she can walk 1 mile in 15 minutes and 120/15 is 8.
Which one is right *Will make BRAINLEST*
Answer:
The correct answer is:
Option A: [tex](14.\frac{1}{7})\frac{2}{5}[/tex]
Step-by-step explanation:
Associative property is applied on three numbers which states that when two numbers are being added or multiplied the order of addition and multiplication doesn't matter i.e. the answer is same.
If a,b and c are three numbers then associative property for multiplication can be given as:
a.(b.c) = (a.b).c
The given expression is:
[tex]14(\frac{1}{7}.\frac{2}{5})[/tex]
Applying the associative property for multiplication we get
[tex](14.\frac{1}{7})\frac{2}{5}[/tex]
Hence,
The correct answer is:
Option A: [tex](14.\frac{1}{7})\frac{2}{5}[/tex]
Which expression is equivalent to (−3n+18m)−(112m−n)?
Answer:
I believe it is -94m-2n
A water tank is in the shape of a right circular cone as shown above. The diameter of the cone is 10 feet, and the height is 15 feet. The shape of the water in the tank is conical with radius r feet and height h feet. At noon, water is leaking from the bottom of the tank at a rate of 12 cubic feet per hour, and the volume of water in the tank is 27π cubic feet. At noon, what is the rate at which the height of the water in the tank is changing? (The volume V of a right circular cone with radius r and height h is V=13πr2h.)
The rate at which the height of water tank changing is [tex]0.4244 \; \text {ft./hr}[/tex]
Step-by-step explanation:
Given information:
[tex]\text{\bold{The diameter of cone}}=10\;\rm{ ft.}[/tex]
[tex]\rm{The\; height\; of\; the\; cone}= 15\;\rm{ ft.}[/tex]
[tex]\text{The rate at which the water is leaking }= 12 \; \rm ft^3/hr.[/tex]
[tex]\text{Volume of water tank}=27 . \pi \; \rm ft^3[/tex]
Now,
If ,we take a right circular cone with radius r and height h , its volume
[tex]\text{volume (V)} = (1/3) \times \pi \times \rm{r^3 \times h[/tex]
Now, the radius of cone when the volume of water tank is given
[tex]\frac{1}{3}\times \pi \rm\times{r^2 \times h = 27 \times \pi[/tex]
The ratio of height to radius of the cone :
[tex]\text {h/r} =3[/tex]
[tex]\text r = \text h/3[/tex]
Now calculate :
[tex]dV/dt= dV/dh \times dh/dt[/tex]
Which gives:
[tex]12 = \frac{d(\text h^3/27 \pi)}{dh} \times \frac{d\text h}{dt} \\\\\frac{d\text h}{dt} = \frac{12}{\pi \text h^2/9}[/tex]
As ,
[tex]27=\frac{1}{27 \times h}[/tex]
[tex]\text h^3=27^2\\\text h= 9\\[/tex]
Now,
[tex]dh/dt=12/(\pi.\text h^2/9)\\dh/dt=4/3\pi\\dh/dt=0.4244\\[/tex]
Hence, The rate at which the height of water tank changing is [tex]0.4244 \; \text {ft./hr}[/tex]
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At a sporting goods store, the price of a bicycle is $650. During a sale, this price is marked down 45%. What is the sale price of the bicycle? Enter your answer in the box. $
Answer:
$357.5
Step-by-step explanation:
Answer:
347.50
Step-by-step explanation:
you have to put the 0 at the end i didnt and got it wrong.
A container of water holds 128 fluid ounces. Toya drinks 8 fluid ounces of water every hour. How many fluid ounces are in the container after 8 hours
Answer: 64 fluid ounces
Step-by-step explanation:
Amount of water in the container = 128 fluid ounces
Amount drank by Toya every hour = 8 fluid ounces
For 8 hours, Toya would have drank:
= 8 × 8 fluid ounces
= 64 fluid ounces
To calculate the amount of fluid ounces
thataree in the container after 8 hours, we then subtract 64 fluid ounces from 128 fluid ounces. This will be:
= 128 fluid ounces - 64 fluid ounces
= 64 fluid ounces
how to convert root into decimal
Pls help me I have no idea
Answer:
130 degrees
Step-by-step explanation:
ABF and BFE are alternate angles. So BFE is 65
BG=FG so FBG is 65. x the exterior angle is 65+65=130 degrees
Help pls help pls help pls help pls help pls
Answer:
It might be b (the second one)
slope= 1/4, y intercept=2
What are the domain and range of x= -2?
Answer:
The range is all real numbers, because it's a vertical line, and the domain is -2 because it's a vertical line with -2 as it's only x.
Step-by-step explanation:
Find the equation of a line that passes through the points (6,7) and (8,3).
Leave your answer in the form
y = mx + c
Answer:
y=-2x+19
Step-by-step explanation:
For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form: m= [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].
Now we have,
m= 3-7/8-6
m=-2. Since m=-2, the equation is y=-2x+b.
To find b, think about what your (x,y) points mean:
(6,7). When x of the line is 6, y of the line must be 7.
(8,3). When x of the line is 8, y of the line must be 3.
Substitute them to the equation y=-2x+b.
You can use either (x,y) point you want..the answer will be the same:
(6,7). y=mx+b or 7=-2 × 6+b, or solving for b: b=7-(-2)(6). b=19.
(8,3). y=mx+b or 3=-2 × 8+b, or solving for b: b=3-(-2)(8). b=19.
So, the equation of the line that passes through the points
(6,7) and (8,3) is y=-2x+19.
Jayden drives 22.5 miles in 30 minutes. If he drove one hour in total at the same rate, how far did he go? Before you try that problem, answer the question below. How many minutes did Jayden drive in total?
Answer:
Step-by-step explanation:
2
A line has a slope of 2 and passes through the point (0,0) what is its equation in slope intercept form
Answer:
y=mx+b is slope-intercept form
where m is the slop, and b is the y intercept
if m is the slop then we can plug that into the equation
y=2x+b
next plug in the y intercept which is 0. the y intercept is the y ok the given point. in the point the y is zero making your intercept 0.
y=2x+0
eliminate the 0
y=2x is your equation
Step-by-step explanation:
Which question can be answered using the expression 1/3÷ 3/4
Answer:
Jillian had a cake and Ruby ate 2/3 of it. Jillian's friends then came over and consumed 3/4 of the kuchen, which Ruby already ate out of. How much of the cake is left?
Step-by-step explanation:
Just think about it with simpler numbers. What if the expression was (4 ÷ 2)? Then the word problem could be made quite easily. Following the previous example, simply replace the numbers (4 and 2) with the fractions given (1/3 and 3/4) and make a few tweaks for it to make more sense.
Good luck!
The total pizza left is 1/3 of the whole pizza. If the remainig student are to take 3/4 of the remaining, how much will each student take
Word problems involving equationsAlgebraic equations are ways we can solve real life apllications.
Given the division problem
1/3÷ 3/4
This can be written usng this statement:
The total pizza left is 1/3 of the whole pizza. If the remainig student are to take 3/4 of the remaining, how much will each student take
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8 1/6 - 2 7/8 =
ANSWER ASAPPP .... AND ILL MARK BRAINLIEST
Answer:
5 7/24
Step-by-step explanation:
Answer:
5.29
Step-by-step explanation:
solve the equation 4x²+4x+1=0
Answer: x = -1/2
4x² + 4x + 1 = 0
⇔ (2x + 1)² = 0
⇒ 2x + 1 = 0
⇔ x = -1/2
Step-by-step explanation:
what is the difference between mutiplying and adding polynomials
Answer:
When you add polynomials, you combine only like terms together. When you multiply polynomials, you multiply all pairs of terms together.
Step-by-step explanation:
.
Answer:
adding, subtracting and multiplying polynomials are, basically, the same as adding, subtracting and multiplying numbers. They only difference is that we have a pesky variable to worry about