The transformation of the graph of f to obtain g is described as follows:
The graph of g is a vertical compression of the graph of f by a factor of 6 units.
The object must be dropped at a height of 1.66 feet from the moon so it hits the ground at the same time as on Earth,
What is the transformation?The functions in the context of this problem are given as follows:
f(t) = -16t² + 10.g(t) = -8/3t² + 10.The multiplier that was applied to function f(t) to obtain function g(t) is given as follows:
-16x = -8/3
16x = 8/3.
x = 8/48
x = 1/6.
The leading coefficient was divided by 6, meaning that the graph of g is a vertical compression of the graph of f by a factor of 6 units.
When does the object hits the ground?The object hits the ground when the output of the quadratic function assumes a value of zero.
For the Earth, we have that the time to hit the ground is obtained as follows:
-16t² + 10 = 0
16t² = 10
t² = 5/8
[tex]t = \sqrt{\frac{5}{8}}[/tex]
t = 0.79 seconds.
For the Moon, the function is given as follows:
g(t) = -8/3t² + h.
In which h is the initial height.
We want that g(t) = 0 when t = 0.79, hence the initial height is obtained as follows:
0 = -8/3(0.79)² + h
h = 8/3(0.79)²
h = 1.66 feet.
More can be learned about transformations at https://brainly.com/question/29209050
#SPJ1
Solve the equation.
1. for parentheses:
distribute
4-2(x+7) =
3(x+5)
2. if necessary:
combine terms
3. apply properties:
add subtract
multiply
divide
4. to start over:
reset the
The value of equation 4-2(x+7)=3(x+5) is that x=-5/7.
Given equation 4-2(x+7)=3(x+5)
We are required to solve the equation for the value of variable x.
Equation is relationship between two or more variables expressed in equal to form.Equation of two variables looks like ax+by=c. It can be a linear equation,quadratic equation, cubic equation. It can be solved for finding the value of variables.
The given equation is 4-2(9x+2)=3(x+5)
It is a linear equation.
We have to first remove the brackets by multiplying the numbers to inside numbers.
4-18x-4=3x+15
Now collect variable x at one end and constant at other end.
-18x-3x=15-4+4
-21x=15
x=-15/21
x=-5/7
Hence the solution of equation 4-2(x+2)=3(x+5) is that x=-5/7.
Learn more about equation at https://brainly.com/question/2972832
#SPJ4
PLSSS THIS NEEDS TO BE DONE QUICKLY
Answer: 433.33 cm^3
Step-by-step explanation: Since the base is a square, volume = base area × height / 3
10*10 = 100, 100 * 13 = 1300, divided by 3 = 433.33 cm^3
O Work out the length of x.
Give your answer rounded to 3 significant figures.
12.4 mm
8.6 mm
X
Answer:
8.9mm
Step-by-step explanation:
To solve for x, we use the Pythagoras theorem.
Pythagoras theorem states that in a right angled triangle, the square of the Hypotenus is equal to the sum of the square of the other two sides.
The Hypotenus is the longest side, or the side facing the right angle.
From the question above,
[tex]12.4 {}^{2} = \: 8.6 {}^{2} + x {}^{2} \\ \\ 153.76 \: = 73.96 \: + x {}^{2} \\ \\ collecting \: liketerms \\ \\ x { \: }^{2} = 153.76 - 73.93 \\ = 79.83 \\ \\ squareroot \: bothsides \\ \\ \sqrt{x {}^{2} } = \sqrt{79.83} \\ \\ x = 8.9[/tex]
Find the length of the segment indicated. Assume that lines which appear to be tangent are tangent. Round to one decimal place if necessary.
Answer: 13.6
Step-by-step explanation: Use a theorem which exists s. then you use pythagoreom
The length of the segment indicated is 13.6
Finding the length of the segment indicated.From the question, we have the following parameters that can be used in our computation:
The circle
Assuming that lines which appear to be tangent are tangent, we have
?² = (2 * 6)² + 6.4²
Evaluate
?² = 184.96
So, we have
? = 13.6
Hence, the length of the segment indicated is 13.6
Read mroe about circle at
https://brainly.com/question/32192505
#SPJ6
how many 2/7 are 150
Answer:
42.8571
Step-by-step explanation:
We would need to divide 150 by 7 and multiply it by 2 to get the answer.
150/7 = 21.42857
21.42857*2 = 42.8571
Representing a Graph with a Slope-Intercept Equation
-5-4-3-2
5
4
3
2
+
2345
y
2 3 4
X
5
A function f(x) is graphed.
What is the slope of the function?
m
What is the y-intercept of the function?
b = v
Which equation represents the graph of the function?
Answer:
1.) The slope is 2
2.) The y-intercept is (0,1)
3.) y = 2x + 1
Step-by-step explanation:
1.) you can either use rise over run or the slope formula. rise over run is quicker, but here's the formula:
you can use any two points on the line, i chose (2, 5) and (1, 3)
[tex]\frac{(y_{2}-y_{1})}{(x_{2}-x_{1})} \\[/tex]
[tex]\frac{3-5}{1-2} \\\\\frac{-2}{-1} \\\\\frac{2}{1} \\\\2[/tex]
2.) for the y-intercept, you just look for the point where the graph crosses the y-axis and x = 0
3.) using the formula y = mx + b, m being the slope and b being the y-intercept, you take the information above and plug it in to get y = 2x + 1
i hope this helped!
NL and MK are diameters of circle J.
Circle J is shown. Line segments M K and N L are diameters. Line segment J P is a radius. Angle M J N is 62 degrees and angle N J P is 90 degrees.
Complete the statements about circle J.
Arc M P is a
and measures
degrees.
Arc M L N is a
and measures
degrees.
Arc M P is a minor arc and measures 152°
Arc M L N is a major arc and measures 298° .
Given that NL and MK are diameters of circle J.
Size of arc MP is 62+90=152°, since MP is smaller than MLN
then it is a minor arc. Hence the correct statement is:
M P is a minor arc and measures 152°.
Size of M L N is 360-62=298°, thus it is a major arc. Hence the
correct statement is:
MLN is major arc and measures 298°.
Arc M P is a minor arc and measures 152°
Arc M L N is a major arc and measures 298° .
learn more about arcs here:
https://brainly.com/question/228276
#SPJ1
Answer:
Complete the statements about circle J.
Arc M P is a
✔ minor arc
and measures
✔ 152
degrees.
Arc M L N is a
✔ major arc
and measures
✔ 298
degrees.
Step-by-step explanation:
edge 2022
Let tan(x)=2/5
What is the value of tan(2π−x)
please!
Answer:
-0.4 or [tex]\frac{-2}{ 5}[/tex]
Step-by-step explanation:
[tex]tan^-^{1} ({\frac{2}{5} })=21.80\\[/tex]
tan ( 2π-21.80)
but 2π = 360
Therefore our question becomes:
tan ( 360-21.80)=tan(338.2)= -0.4
PLEASE HELP I've been struggling on this one :(
Answer: The answer is (x+2)(x-4)(x-4)
Or as a short form you can write it as [tex](x+2) (x-4)^{2}[/tex]
Step-by-step explanation:
Answer is very lengthy but I am 100% sure that's the correct answer
Answer:
(x³ - 6x² + 32) = (x - 4)²(x + 2)
Step-by-step explanation:
(x³ - 6x² + 32)/(x - 4) =
x² - 2x - 8
----------------------------------
x - 4 | x³ - 6x² + 0x + 32
x³ - 4x²
----------
-2x² + 0x
-2x² + 8x
----------------
-8x + 32
-8x + 32
-------------
0
(x³ - 6x² + 32) = (x - 4)(x² - 2x - 8) = (x - 4)(x - 4)(x + 2) =
= (x - 4)²(x + 2)
The graph shows the speed of a cart over a period of several minutes. At approximately what time did the speed of the cart begin to decrease?
The speed of the cart begin to decrease at approximately: 3.5 minutes.
What is a Time-Speed Graph?A typical time-speed graph shows the time on the x-axis and the speed on the y-axis. When the slope is rising, it means the speed is increasing. When the slope is horizontal, it means the speed is constant. When the slope falls or decline, it means speed is decreasing.
We are given a time-speed graph that shows the speed of a cart over a period of several minutes. Time in minutes is on the x-axis (horizontal axis) while speed in miles per hour is on the y-axis (vertical axis).
From the graph given, the speed of the cart started increasing up to about 3 minutes, since the line slopes upwards. Then, between 3 and 4 minutes, we have a horizontal line which starts to decline at approximately 3.5 minutes.
Therefore, we can conclude that the speed of the cart begin to decrease at approximately: 3.5 minutes.
Learn more about time-speed graph on:
https://brainly.com/question/3480245
#SPJ1
Two random samples were done to determine how often people in a community go to the dentist. the first sample surveyed 10 people as they entered their workplaces. the first sample found that the mean time between visits to the dentist was 7.5 months. the second sample surveyed 50 people as they entered the local grocery store. the second sample found that the mean time between visits to the dentist was 18.1 months. which statements are true? check all that apply. the first sample is likely to be more representative of the population. the second sample is likely to be more representative of the population. the second sample will give a better representation because it is larger. the first sample is not biased. community members probably visit the dentist about once every 18 months.
Answer:
B, C and E
Step-by-step explanation:
If x = 3 (y 2) minus 1 what is the value of w in terms of x and y? w = startfraction x minus 3 y over 3 endfraction w = startfraction x minus 3 y 1 over 3 endfraction w = x minus 3 y 1 w = startfraction x 1 over 9 y endfraction
The value of w from the given equation is w=(x-3y+1)/3.
Given an equation x=3(y+w)-1 and we have to find the value of w in terms of x and y.
Equation is relationship between two or more variables expressed in equal to form. Equation of two variables look like ax+by=c. It may be linear equation, quadratic equation,cubic equation.
The given expression is x=3(y+w)-1 and we have to find the value of w. To find the value we have to first solve the right side of the equation.
x=3y+3w-1
Now take w at one end and all other variables in other end.
3w=x-3y+1
Now divide both sides by 3.
3w/3=(x-3y+1)/3
Now cancel 3 from numerator and denominator in left side.
w=(x-3y+1)/3
Hence the value of w in the equation x=3(y+w)-1 is w=(x-3y+1)/3.
Learn more about equation at https://brainly.com/question/2972832
#SPJ1
Which equation is equivalent to 3[x + 3(4x – 5)] = 15x – 24?
15x – 15 = 15x – 24
15x – 5 = 15x – 24
39x – 45 = 15x – 24
39x – 15 = 15x – 24
The equivalent equation of the given equation is 39x - 45 = 15x - 24.
Hence, option C) is the correct answer.
What is the equivalent of the given equation?Given the equation; 3[x + 3(4x – 5)] = 15x – 24
We expand and collect like terms
3[x + 3(4x – 5)] = 15x – 24
3( x + 12x - 15 ) = 15x - 24
3x + 36x - 45 = 15x - 24
We add the like terms on both sides
39x - 45 = 15x - 24
Therefore the equivalent equation of the given equation is 39x - 45 = 15x - 24.
Hence, option C) is the correct answer.
Learn more about equations here: brainly.com/question/14686792
#SPJ1
when evaluating (6.28x10^12)\(3.14x10^4)
Answer:??? rest of the question I think is what will be the exponent of 10 in the quotient? answer is 8
Step-by-step explanation:
I keep believing the answer is either 18,000 or 1,800 but im incorrect. Can someone please help me?? I use the formula A^2 *2*A*L=SA
The base is a square, so the area of the square is (10 cm)² = 100 cm²
To find the area of each triangle use the formula
base • height
10 cm • 9 cm = 90 cm²
now multiply by the number of triangles
90 cm • 4 = 360 cm²
Add the area of the square:
100 cm² + 360 cm² = 460 cm²
I hope it's correct
Answer:
SA = 280 cm²
Step-by-step explanation:
SA = area of base + area of 4 congruent triangles
= 10² + (4 × [tex]\frac{1}{2}[/tex] × 10 × 9 )
= 100 + (2 × 10 × 9)
= 100 + 180
= 280 cm²
The length of one leg of an isosceles right triangle is 3 ft. What is the perimeter of the triangle?
O3+3√√2 ft
O 3+3-√√3 ft
O 6+3 √√2 ft
O6+3√3 ft
Step-by-step explanation:
Solution
verified
Verified by Toppr
Correct option is A)
In an isosceles right angled triangle, the two sides on the right angle are equal.
Let the equal sides be a.
Hence, hypotenuse of the isosceles right angled triangle =
a
2
+a
2
=
2
a
Given, perimeter of the triangle =(6+3
2
)m
⇒a+a+
2
a=(6+3
2
)m
⇒a(2+
2
)=3(2+
2
)m
⇒a=3m
In the isosceles right triangle, the base and height =a
Hence, area of the triangle =
2
1
×base×height =
2
1
×3×3=4.5m
2
Some articles were bought at 6 for rupees 5 and sold at 5 for rupees 6. find the gain percent
44% is the answer
6 Article price at buying =5 Rs
1 Article price at buying = 5/6...(i)
5 Articles sold at Rs. 6
1 Articles cost at sold = 6/5 ....(ii)
% Gain=((6/5 - 5/6)/ 5/6) * 100
= 11/25 * 100 = 44%
Profit is a general increase in an asset or the value of an asset. If the item's current price is higher than the original purchase price, you will make a profit. For accounting and tax purposes, profits can be categorized in several ways: B. Gross profit and net profit, or realized profit and unrealized (paper) profit.
The definition of victory is profit, benefit, or increase. An example of profit is a 5% increase in income over the past year. An example of a win is a 5 point lead over another team.
Learn about profit here:https://brainly.com/question/933169
#SPJ4
WILL MAKE BRAINLIEST!! What type of angle is angle A?
Answer:
Step-by-step explanation:
Obtuse, greater than 90 degrees
Answer:
It should be an obtuse angle
Step-by-step explanation:
Well, it just is
Find the equation of the linear function represented by the table below in slope-intercept form.
Answer:
y=-2x+3
Step-by-step explanation:
Use the slope formula
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
According to the table, x=1 and y=1. There is another point x=2 and y=-1.
We can say that [tex]x_{1}=1[/tex] and [tex]y_{1} =1[/tex]. We can also say that [tex]x_{2}=2[/tex] and [tex]y_{2}=-1[/tex]. Plugging this into the equation we get:
[tex]m=\frac{-1-1}{2-1}=-2[/tex].
This means that the slope of your equation is -1/2
Point intercept form is y=mx+b
So plugging the slope in we have [tex]y=2x+b[/tex]
We can plug in one of the values from the value table for x and y, but to keep things simple, I’m going to just use x=1, and y=1, the first values on the table. Plugging these into the equation we get:
[tex]1=-2(1)+b\\ 1=-2 +b\\b=1+2 \\b=3[/tex]
So our equation is [tex]y=-2x+3[/tex]
What is the perimeter of the trapezoid
The perimeter of the trapezoid is 18 lines
How to determine the perimeterFormula for perimeter of a trapezoid is given as;
Perimeter = a + b+ c + d
a = 1
b = 4
c = 4
d = 9
Perimeter = 1 + 4 + 4 + 9
Perimeter = 18
Thus, the perimeter of the trapezoid is 18 lines
Learn more about a trapezoid here:
https://brainly.com/question/1463152
#SPJ1
find the slope of the line on the graph
Answer:
4
Step-by-step explanation:
Slope=rise/run
there is a increase of 4 in y for every increase of 1 in x
slope:
y-intercept:
HELP PLS
20 points
Answer:
slope = - 1 , y- intercept = 2
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with ( x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (2, 0) ← 2 points on the line
m = [tex]\frac{0-2}{2-0}[/tex] = [tex]\frac{-2}{2}[/tex] = - 1
the y- intercept is the point on the y- axis where the line crosses , so
y- intercept = 2
Answer:
Slope: -1
Y-intercept: 2
Step-by-step explanation:
The line crosses the y-axis at 2. and the slope would be -1 since going down by one unit, and the line going down would mean that it is negative.
I hope it helps! Have a great day!
bren~
In geometry, Heron's formula (sometimes called Hero's formula), named after Hero of Alexandria, gives the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin, contrary to other formulas for the area of a triangle, such as half the base times the height. Use Heron's formula to find the area, in square meters, of ΔABC.
a=7m, b=5m, c=6m
Answer: S=6√6 m².
Step-by-step explanation:
Heron's formula
[tex]\displaystyle\\\boxed {S=\sqrt{p*(p-a)(p-b)(p-c)} }[/tex],
a, b, c - sides of a triangle,
[tex]\displaystyle\\p=\frac{a+b+c}{2}[/tex]
S - triangle area.
a=7 m, b=5 m, c=6 m.
[tex]p=\frac{7+5+6}{2} \\p=\frac{18}{2} \\p=9 (m).[/tex]
Hence,
[tex]S=\sqrt{9*(9-7)*(9-5)*(9-6)}\\S=3*\sqrt{2*4*3}\\S=3*2*\sqrt{2*3} \\S=6\sqrt{6} \ (m^2).[/tex]
I need help anyone with graphs
The given function shows imply that the graph g(x) is shifted two units right and three units up.
Option B is correct.
What is the transformation of a function?The transformation of a function occurs in a fancy way such that a function maps itself. f: x → x.
From the given information:
Let's take a look at the function f(x) that goes through 0 just when x = 0. Now we want to move it to the right by 2. It implies that it has to go through 0 when x = +2.
Now, we have to add 2 to x, then the function becomes f'(x) = f(x-2) will be shifted by 2 units to the right.
Similarly, the same scenario occurs when shifting up. Again imagine your function passes 0 when x = 0. We have to add 3. Now, the function f’’(x) = f(x) + 3 will be shifted by 3 units up.
Combining the two transformations, we have:
g(x) = f(x-2) + 3Therefore, we can conclude that the function implies that the graph g(x) is shifted two units right and three units up.
Learn more about the transformation of functions here:
https://brainly.com/question/1548871
#SPJ1
The center of circle q has coordinates (-2, 1). if circle q passes through r (6, 7), what is the length of its diameter?
There are multiple strategies we can use to find the diameter of a circle. For this question, we must calculate the length of the radius first and multiply by 2 to find the diameter.
Solving the QuestionWe're given the centre and a point on the circumference: [tex](-2,1),(6,7)[/tex].
Find the distance between them using the distance equation:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Plug in the given points:
[tex]d=\sqrt{(-2-x_1)^2+(1-y_1)^2}\\d=\sqrt{(-2-6)^2+(1-7)^2}\\d=\sqrt{(-8)^2+(-6)^2}\\d=\sqrt{64+36}\\d=\sqrt{100}\\d=10[/tex]
Therefore, the radius of the circle is 10 units.
Multiply the radius by 2 to find the length of the diameter:
10 × 2
= 20
Therefore, the length of the diameter is 20 units.
Answer20 units
A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. What is the dependent variable
Using variable concepts, of dependent and independent variables, it is found that the dependent variable is the amount of sales dollars earned.
What is the relation between a function and the dependent and independent variables?A function has the following format: y = f(x).In which each value of y is a function of one value of x, and thus, x is the independent variable and y is the dependent variable.That is, the input of the function is the independent variable and the output is the dependent variable.In this problem, the manager believes that the amount of sales dollars earned is a function of the number of contacts that the salesperson makes, hence:
The number of contacts is the independent variable.The amount of sales dollars earned is the dependent variable.More can be learned about dependent and independent variables at https://brainly.com/question/1429012
#SPJ1
how do you solve (a²-28)÷(a-5)
Answer:
Divide the highest order term in the dividend a2a2 by the highest order term in divisor aa.Step-by-step explanation:
<3Find the value of X. Round to the nearest tenth HELP ASAP!!!!
Answer: 22.5
Step-by-step explanation:
[tex]\sin 64^{\circ}=\frac{x}{25}\\\\x=25 \sin 64^{\circ}\\\\x \approx 22.5[/tex]
HELP HELP HELP
HELP HELP HELP
HELP HELP HELP
(DIVISION) NO SYNTHETIC DIVISION NOR FACTORING
STEP BY STEP
Answer:
[tex]2x - 3 + \frac{1}{x-1}[/tex]
Step-by-step explanation:
Attachment :)
We use long division
Help me with this question please