the transformations used are:
Dilation of scale factor 5.Shift of 2 units to the right.Shift of 3 units up.Which transformations are used?
We start with the function:
[tex]f(x) = 2^x[/tex]
And we have the transformed function:
[tex]g(x) = 5*2^{x-2} + 3[/tex]
Bow, let's start with the original function f(x). If first we apply a vertical dilation of scale factor 5, then we have:
g(x) = 5*f(x).
Then we apply a shift of 2 units to the right, so we have:
g(x) = 5*f(x - 2)
Then we apply a shift of 3 units up, so we have:
g(x) = 5*f(x - 2) + 3
Replacing f(x) by the actual function:
[tex]g(x) = 5*2^{x-2} + 3[/tex]
Then the transformations used are:
Dilation of scale factor 5.Shift of 2 units to the right.Shift of 3 units up.If you want to learn more about transformations:
https://brainly.com/question/4289712
#SPJ1
The diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5cm². calculate correct to 3 Significant figures, the base radius, r ,height h Volume of the cone [take π 22/7]
The volume of the cone is V = 381.15 cu.cm
What is the Curved Surface Area of the cone ?The curved surface area of the cone is given by
A = πrl
The slant height given in the question is
l = 10.5 cm
A = 115.5 sq.cm
radius = ?
Height = ?
Volume = ?
Using the Curved Surface Area Formula
115.5 = π * r * 10.5
taking π = 22/7
r = 3.5 cm
The slant height is given by
[tex]\rm l = \sqrt{ r^2 + h^2}[/tex]
Therefore the height is
[tex]\rm h = \sqrt{ 10.5^2 -3.5^2}[/tex]
h = 9.9 cm
The volume of the cone is
V = π r²h
V = (22/7) * 3.5 * 3.5 * 9.9
V = 381.15 cu.cm
The volume of the cone is V = 381.15 cu.cm
To know more about Volume
https://brainly.com/question/1578538
#SPJ1
prove that (1- cos(pi)/(8))(1-cos(3 pi)/(8))(1-cos(5 pi)/(8))(1=cos(7 pi)/(8))=(1)/(8)
Step-by-step explanation:
1&$)&(5$6$5*-_+_7&'+&-^€=%
solve X/3 + 5/2 = -3/2 pls pls
Answer:
X=-12
Step-by-step explanation:
Subtract -5/2 on both sides:
X/3+5/2-5/2=-3/2-5/2
X/3=-8/2
X/3=-4
Multiply both sides by 3:
X/3*3=-4*3
X=-12
Answer:
x = -12
Step-by-step explanation:
To solve for x, we always want to isolate x {isolate = getting it by itself}
So, for the equation: X/3 + 5/2 = -3/2
we should first get x on its own side:
[tex]\frac{x}{3}+\frac{5}{2}=-\frac{3}{2}[/tex]
[tex]-\frac{5}{2}[/tex] [tex]-\frac{5}{2}[/tex] {subtract 5/2 from both sides} {-3/2 - 5/2 = -8/2}
[tex]\frac{x}{3} = -4[/tex]
×3 ×3 {multiply both sides by 3 to find "1"x}
x = -12
check:
-12/3 + 5/2 = -3/2
-4 + 5/2 = -3/2
(5/2 = 2 [tex]\frac{1}{2}[/tex] ; 2 [tex]\frac{1}{2}[/tex] - 4 = -1 [tex]\frac{1}{2}[/tex])
-1 [tex]\frac{1}{2}[/tex] = -3/2 {3/2 = 1 [tex]\frac{1}{2}[/tex]}
-1 [tex]\frac{1}{2}[/tex] = -1 [tex]\frac{1}{2}[/tex]
{TRUE}
so, x = -12
hope this helps!!
Tara has a box of 908 beads for making bracelets. She wants to put 15 beads on each bracelet she makes. What is the greatest number of bracelets Tara can make with these beads? Tara has a box of 908 beads for making bracelets . She wants to put 15 beads on each bracelet she makes . What is the greatest number of bracelets Tara can make with these beads ?
Answer:
Tara can make 60 bracelets.
Step-by-step explanation:
908 / 15 = 60.5
this is hard for me could smone help me ASAP please?
Answer:
x is 90°
y is 56°
Step-by-step explanation:
Concepts used :
The angle subtended by a diameter inside the circle is always 90° .
Sum of interior angles of a triangle is 180°.
Here x is the angle subtended by the diameter of the circle therefore ,
x is 90°.
let the end points of diameter as A , B
and the point where the it subtends the 90° angle be C
using interior angle property on the triangle ΔABC
90° + 62° + ∠A = 180°
152° + ∠A = 180°
∠A = 180° - 152°
∠A = 28°
now let he midpoint of diameter as D
as the sides DC and DA are radius of circle and therefore equal
so using isosceles triangle property which states that angle opposite to equal sides are equal
so the angle ∠ACD = 28°
now using exterior angle property on ΔADC
y = 56°
learn more about triangles on
https://brainly.com/question/2773823
#SPJ10
Question 4 (Essay Worth 10 points)
(05.06; 05.07 MC)
A prism and two nets are shown below:
Image of a right triangular prism and 2 nets. The triangle bases have base 4, height 3, and diagonal side 5. The length of the prism from the bases is 8.6. Net A has 3 rectangles in a row. The middle one has sides AC and CD. This middle one has triangle ABC on top and identical triangle below. Net B is the same except that the triangle base ABC is on top of the last rectangle which has sides AC and CD. Units are in inches.
Part A: Which is the correct net for the prism? Explain your answer. (2 points)
Part B: Write the measurements of Sides AB, BC, and CD of the correct net. (4 points)
Part C: What is the surface area of the prism? Show your work. (4 points)
Answer:
115.2 in^2
Step-by-step explanation:
total surface area Stot = 113.2 in2
lateral surface area Slat = 103.2 in2
top surface area Stop = 6 in2
bottom surface area Sbot = 6 in2
Choose the variable expression that matches this phrase.
the sum of the number of crew members on the tour boat and the 5
passengers.
A. 5-c
B. 5c
C. 5+ c
D. 5÷c
The sum of the number of crew members (c) on the tour boat and the 5 passengers is 5 + c. Then the correct option is C.
What is an equivalent expression?The equivalent is the expressions that are in different forms but are equal to the same value.
The sum of the number of crew members (c) on the tour boat and the 5 passengers.
This can be written as in the form of the mathematical form.
⇒ 5 + c
Then the correct option is C.
More about the equivalent link is given below.
https://brainly.com/question/889935
#SPJ1
The coordinates of the vertices of △HIJ are H(−2,2), I(8,−2), and J(−4,−3). Identify the perimeter of △HIJ to the nearest tenth
Answer:
28.2
Step-by-step explanation:
The perimeter of a plane figure is the sum of the lengths of its sides. Those lengths and their sum can be found a number of different ways.
__
graphing aidThe values computed by the graphing program in the attachment add up to 28.2 units.
__
using algebraThe length of each side of the triangle can be computed using the distance formula or the Pythagorean theorem. For a given "rise" and "run", the length of a line segment is ...
d = √(rise^2 +run^2)
HI = √((-4)^2 +10^2) = √116 ≈ 10.770
IJ = √(1^2 +12^2) = √145 ≈ 12.042
JH = √(5^2 +2^2) = √29 ≈ 5.385
The perimeter is the total of the lengths of the sides:
P = HI +IJ +JH = 10.770 +12.042 +5.385 = 28.197
To the nearest tenth, the perimeter is 28.2 units.
Triangle rst is dilated by a scale factor of 5 to form triangle r's't'. side r's' measures 40. what is the measure of side rs?
Answer: 8
Step-by-step explanation:
We know that scale factor = (image)/(preimage).
Substituting in what we have,
[tex]5=\frac{R'S'}{RS}\\\\5=\frac{40}{RS}\\\\RS=\boxed{8}[/tex]
Answer:
Step-by-step explanation:
We know that r's't' was formed by a scale factor of 5.
This means rst was multiplied by 5 to create r's't'.
Dividing the sides of r's't' by 5 will give us the sides of the
pre-image. If r's' = 40 - dividing 40 by 5 = 8.
So rs is 8.
Members of a lacrosse team raised $2412.50 to go to a tournament. They rented a bus for $1072.50 and budgeted $67 per player for meals. Determine the number of players the team can bring to the tournament. Please step by step
Answer:
20 Players
Step-by-step explanation:
Total Amount of Money: $2412.50
First the team rented us a bus for $1072.50
Subtract the bus from the total
$2412.50 - $1072.50 = $1340
Total Amount of Money after bus: $1340
From there we need to find the max number of players that can go.
The budget cost for each player is $67.
So we divide the remaining money by $67 to find the number of players that can go.
$1340/$67 = 20 Players.
Please mark brainliest and click thanks.
Hope this helps!
Use the drawing tools to form the correct answer on the graph. Graph the line that represents this equation: y=-5x+2
An equation is formed of two equal expressions. The graph for the given situation can be drawn as shown below.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.
The graph for the given equation y=-5x+2 can be drawn as shown below.
Learn more about Equation:
https://brainly.com/question/2263981
#SPJ1
Fluffy the bunny ate 1/2 of a carrot in the morning, and he ate some more at night. By the end of the day, he still had 1/3 of the carrot left to eat. How much of the carrot did Fluffy the bunny eat at night?
Answer:
1/6
Step-by-step explanation:
the total carrot is 1/1 and fluffy ate 1/2 of it . this means half has been eaten and it is left with half so now 1/2 -1/3 ( carrot left in the morning - the carrot left now ) this will be 1/6
HELP PLEASE!!!!!!!!!!!!!!!!!!!
Answer:
D.) x - 4
Step-by-step explanation:
This is a graph of an exponential/quadratic function. There general structure looks like this:
ax² + bx + c
Generally, when finding the zeros these functions, you are told to factor the equation. Once you have factored the equation, you can set the factors equal to zero to find the points where the function touches the x-intercept.
That being said, you can determine the factors without having the entire equation by identifying the zeros on the function. On this graph, there is a zero at (4,0). This means that one of the factors must have been "x - 4". You can check your work by setting the factor equal to zero.
x - 4 = 0
x = 4
Pls help!!!!!!!!!!!!!!!!
Answer:
D: 6.5, 3
C: 23.5, 9
I think
Answer:
C (23.5, 9)
D (6.5, 3)
Rectangular prism with a length, width, and height of 3/5 cm, 4/5cm, and 3/5 cm, respectively
The volume of the rectangular prism is 36/125 cm³.
What is the volume?A rectangular prism is a three-dimensional shape. It also known as a cuboid.
Volume = length x width x height
3/5 x 4/5 x 3/5 = 36/125 cm³
Here is the complete question :
Rectangular prism with a length, width, and height of 3/5 cm, 4/5cm, and 3/5 cm, respectively. Find its volume?
To learn more about rectangular prisms, please check: https://brainly.com/question/8890358
#SPJ1
Loss = 10% VAT=13% SP WITH VAT=25,425 now calculate CP
The cost price of the product will be 25000.
How to calculate the price?From the information given, the cost price is 25000. The loss is 10%. This will be:
= 25000 - (10% × 25000)
= 25000 - 2500
= 22500
The tax is 13%. This will be:
= 22500 + (13% × 22500)
= 22500 + 2925
= 25425
Learn more about price on:
brainly.com/question/1153322
#SPJ1
i need help filling in the blanks
Complete the steps to solve the equation above.
2x + 5 = 4x - 1
+ +
After adding on both sides, the equation looks like this:
2x + = 4x
Now it's time to the combine like terms and .
2x + = 4x
- -
After subtracting on both sides, the equation looks like this:
=
Finally, we divide by on both sides, and we have solved the equation!
x is equal to .
The 3 steps to solve the algebra equation have each sub step as explained and written below.
How to solve algebra problems?We are given the algebraic equation;
2x + 5 = 4x - 1
Step 1; After adding 1 to both sides, we have;
2x + 5 + 1 = 4x - 1 + 1
2x + 6 = 4x
Step 2; We subtract 3x from both sides to get;
2x - 2x + 6 = 4x - 2x
2x = 6
Step 3; Divide both sides by 3 to get;
2x/2 = 6/2
x = 3
Read more about solving algebra problems at; https://brainly.com/question/4344214
#SPJ1
Shape R is reflected in
a) What are the coordinates of C'?
Then R' is translated by (-3)
-6
R
=
-5 -4 -3 -2 -1
b) What are the coordinates of C"?
Y
5+
4-
3-
2+
1
- 1 to give R'.
-1-
-2-
--3-
-4-
--5+
1
to give R".
2
3 4
sit
5
X
The new coordinates of C is (-5,2), (-5,5) (-7,3) (-7,5)
The correct question is
Shape R is reflected in x axis and is translated by (-3, 0) , What will be the coordinates of the new figure
The figure is attached with the answer.
What happens when a figure is reflected on an axis ?When a figure is reflected along any axis , the coordinate of the axis on which it is reflected remains the same while the other coordinate vis the additive inverse of the given coordinate
It is given that the coordinate point of R
(-2 ,-2) , (-2,-5) (-4,-3) (-4,-5)
When it is reflected along x axis the new coordinates are
(-2 , 2), (-2,5) (-4,3) (-4,5)
and when translated by -3,0
(-5,2), (-5,5) (-7,3) (-7,5)
Therefore the new coordinates of C is (-5,2), (-5,5) (-7,3) (-7,5)
To know more about Reflection over an axis.
https://brainly.com/question/15175017
#SPJ1
A sample of substance x that has a mass of 326.0 g releases 4325.8 cal when it freezes at its freezing point. if substance x has a molar mass of 58.45 g/mol, what is the molar heat of fusion for substance x? use q equals n delta h.. 13.31 cal/mol 74.00 cal/mol 775.6 cal/mol 19054.7 cal/mol
The molar heat of fusion for substance X , given the data is 775.6 cal/mol
How to determine the mole of the substance XMass = 326 gMolar mass = 58.45 g/molMole = ?Mole = mass / molar mass
Mole = (326 / 58.45) moles
How to determine the heat of fussionMole (n) = (326 / 58.45) molesHeat (Q) = 4325.8 calHeat of fusion (ΔHf) = ?
Q = n × ΔHf
4325.8 = (326 / 58.45) × ΔHf
4325.8 = (326 × ΔHf ) / 58.45
Cross multiply
326 × ΔHf = 4325.8 × 58.45
Divide both sides by 326
ΔHf = (4325.8 × 58.45) / 326
ΔHf = 775.6 cal/mol
Learn more about heat transfer:
https://brainly.com/question/6363778
#SPJ1
Solve |2x - 6| < 10
{x|-2 < x < 8}
{x|2 < x < 8}
{x|-8 < x < 8}
HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
write and solve a proportion to complete the statement. Round to the nearest hundredth if necessary.
1. 6km ≈ ?mi
2. 2.5 L≈ ?gal
3. 90lb ≈ ?kg
pls help
From unit conversion, it is found the following results:
6km ≈ 3.73 mi
2.5 L≈ 0.66 gal
90 lb ≈ 40.82 kg
Unit Conversion
Units of measurement are part of our daily lives. There are different units for area, length, volume, mass, and others. Because of this, it is important to know converting them.
For solving this question you need some information as:
1 km = 0.621371 mi ( unit for length and distance)
1 L = 0.2641722 gallons (unit for volume)
1 lb = 0.453592 kg (unit for mass)
Therefore,
If 1 km = 0.621371 mi, you will have:1 km -------- 0.621371 mi
6 km -------- x mi
x= 6* 0.621371
x=3.73 mi
Thus, 6km ≈ 3.73 mi.
If 1 L = 0.2641722 gallons, you will have: 1 L-------- 0.2647122 gal 2.5L -------- x gal x= 2.5* 0.2647122 x=0.66 galThus, 2.5 L≈ 0.66 gal.If 1 lb = 0.453592 kg, you will have: 1 lb-------- 0.453592 kg 90 lb -------- x kg x= 90* 0.453592 x=40.82 kgThus, 90 lb≈ 40.82 kg.Read more about unit conversion here:
https://brainly.com/question/13016491
#SPJ1
Think about the zoo meals in another way. Many different foods are prepped in the commissary for the
animals. Though each animal has a very specific combination of foods, there may be foods repeated in diets
for different animals. For example, cabbage may be used in the morning meals for 20 different animals. If
the food is the input, and the animal is the output, is this relationship a function?
Answer:
89
Step-by-step explanation:
Solve the equation for x by graphing.
-2x − 3 = 3x + 2
Find the missing side of each triangle. Leave your answers in simplest radical form.
2√3 m
A) √ 19 m
c) √5 m
O a
a
Ob b
Oc
√7m
C
Od d
B) √17 m
D) √√2 m
Answer:
C [tex]\sqrt{5}[/tex]
Step-by-step explanation:
Use pythagorean theorem.
[tex]x^{2}[/tex] +[tex]\sqrt{7} ^{2}[/tex] = (2[tex]\sqrt{3}) ^{2}[/tex]
[tex]x^{2}[/tex] + 7 = 12 Subtract 7 from both sides
[tex]x^{2}[/tex] = 5 Take the square root of both sides to solve
x = [tex]\sqrt{5}[/tex]
Two piecewise functions are shown below. What is the value of
6f (-2) + 3g (1)?
f(x) =
0-7
O-25
1/3
O 18
{
-3x
*+2'
if x < -2
³, if x ≥-2
(2|x-1| +3,
-5√x+3-1,
g(x) =
={
if x ≤ 1
if x > 2
Step-by-step explanation:
I am not sure what your problem here is.
you understand the inequality signs ?
anyway, to get
6×f(-2) + 3×g(1)
we can calculate every part of the expression separately, and then combine all the results into one final result.
f(-2)
we look at the definition.
into what category is -2 falling ? the one with x<-2, or the one with x>=-2 ?
is -2 < -2 ? no.
is -2 >= -2 ? yes, because -2 = -2. therefore, it is also >= -2.
so, we have to use
1/3 x³
for x = -2 that is
1/3 × (-2)³ = 1/3 × -8 = -8/3
g(1)
again, we look at the definition.
into what category is 1 falling ? the one with x > 2 ? or the one with x <= 1 ?
is 1 > 2 ? no.
is 1 <= 1 ? yes, because 1=1. therefore it is also <= 1.
so we have to use
2×|x - 1| + 3
for x = 1 we get
2×0 + 3 = 3
6×f(-2) = 6 × -8/3 = 2× -8 = -16
3×g(1) = 3× 3 = 9
and so in total we get
6×f(-2) + 3×g(1) = -16 + 9 = -7
this is not the answer i was looking for
Given log subscript 4 baseline 3 almost-equals 0.792 and log subscript 4 baseline 21 almost-equals 2.196, what is log subscript 4 baseline 7?
The value of the logarithmic function log₄7 = 1.404, when the values of the logarithmic functions log₄3 = 0.792 and log₄21 = 2.196.
We are given the logarithmic functions:
log₄3 = 0.792 ,,, (i), and log₄21 = 2.196 ... (ii),
and we are asked to find the value of the logarithmic function log₄7.
On subtracting (i) from (ii), we get:
log₄21 - log₄3 = 2.196 - 0.792.
Using the quotient law of logarithms, according to which:
logₓa - logₓb = logₓ(a/b), we can write the above equation as:
log₄(21/3) = 1.404,
or, log₄7 = 1.404.
Therefore, the value of the logarithmic function log₄7 = 1.404, when the values of the logarithmic functions log₄3 = 0.792 and log₄21 = 2.196.
Learn more about logarithms at
https://brainly.com/question/11707281
#SPJ4
Answer:
A.
1.404
Step-by-step explanation:
1) Which statement is needed to fill in the blank in this syllogism? If two lines are parallel, then ____________________. If the lines never intersect, then the lines have the same slope. Therefore, if two lines are parallel, then the lines have the same slope.
A) the lines have the same slope
B) the lines never intersect
C) the lines have the same equation
D) the lines are continuous
Answer:
B) the lines never intersect
Step-by-step explanation:
okay essentially, syllogism is formatted in a repetitive way
it's something like:
if "a" are "b"
and "b" are "c"
then "a" are "c"
(a = b
b = c
logically, c = a)
(idea, thing related to idea, conclusion relating the two)
hope this helps!!
Answer:
the lines never intersect
Step-by-step explanation:
Syllogisms are connected by a shared statement that connects a hypothesis to a different conclusion.
in a dilation, what is preserved and what is altered?
Answer:
A dilation preserves angle measures.
A dilation alters the length of line segments by the same proportion.
Step-by-step explanation:
A dilatation is a transformation that alters a figure's size while maintaining its shape and orientation. Each linear measure of the figure, such as a side length, is multiplied by the scale factor of a dilatation. A dilation is a transformation where all line segments' lengths are altered uniformly. While a dilatation can alter a figure's size, it cannot alter a figure's form. Dilations are not isometries as the figure's size changes.
Which of the following is most likely the next step in the series?
Answer:
I think the answer is B
Step-by-step explanation:
