The expression of the translated function g(x) is gotten as; g(x) = 2x² - 3
How to Interpret Graph Translations?
We are given the function;
f(x) = 2x² + 3
Now, when we translate a function f(x) downwards, the new function becomes;
g(x) = f(x) - a
where a is the amount of units by which the graph was translated.
Thus for translation of 6 units vertically downwards;
g(x) = 2x² + 3 - 6
g(x) = 2x² - 3
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(03.04 MC) Two pieces of bread, banana and whole wheat, were left out on a kitchen counter and mold began to grow on them. The area of mold growth B(t), in mm2, on the piece of banana bread present after time t weeks, can be represented by the equation B(t) = 20(1.06)t. The area of mold growth W(t), in mm2, present on the piece of whole wheat bread after t weeks is represented in the table. t (in weeks) 1 2 3 4 W(t) (in mm2) 40.8 41.62 42.45 43.30 Which statement best compares the mold growth rates of the banana bread and the whole wheat bread? Question 16 options: The mold growth rate of the banana bread was three times the mold growth rate of the whole wheat bread. The mold growth rate of the banana bread was twice the mold growth rate of the whole wheat bread. The mold growth rate of the banana bread was half the mold growth rate of the whole wheat bread. The mold growth rate of the banana bread was a third the mold growth rate of the whole wheat bread.
Answer:
(a) The mold growth rate of the banana bread was three times the mold growth rate of the whole wheat bread
Step-by-step explanation:
The equation for exponential growth can be written in the form ...
f(t) = a·b^t
where a is the initial value, and b is the growth factor for time period t. The growth factor is related to the growth rate by ...
b = 1 +r . . . . . where r is the growth rate in time period t
__
banana breadThe equation for the area of mold on the banana bread is given as ...
B(t) = 20·1.06^t
Comparing to our generic equation, we see ...
a = 20b = 1.06 = 1 + 0.06The growth rate of the mold on the banana bread is given as 0.06 = 6% per week.
__
whole wheat breadWe are given some values of t and area that we can use to find the growth rate of mold on the whole wheat bread.
W(1) = 40.8 = a·b^1
W(4) = 43.30 = a·b^4
The ratio is ...
W(4)/W(1) = (a·b^4)/(a·b^1) = b^3 = 43.30/40.8
Then the value of b can be found to be ...
b = ∛(43.30/40.8) ≈ 1.02002 ≈ 1 + 0.02
The growth rate of mold on the whole wheat bread is about 0.02 = 2% per week.
__
comparison of growth ratesThe mold growth rate on the banana bread compared to that on the whole wheat bread is ...
(banana bread growth rate)/(whole wheat bread growth rate) = 6%/2% = 3
We can conclude ...
The mold growth rate of the banana bread was three times the mold growth rate of the whole wheat bread
What is the answer to 9!= and 12!=
Answer:
permutation is multiplying numbers from the number given to its last end. so that 9*8*7*6*5*4*3*2*1=is answer. thesame for 12!
Answer:
9! = 362,880
12!=479,001,600
Step-by-step explanation:
the symbol ! simply means factorial
9! = 9×8×7×6×5×4×3×2×1= 362,880
12! = 12×11×10×9×8×7×6×5×4×3×2×1=479,001,600
Which function is represented by the graph?
Answer:
D. f(x) = -|x+4| +3
The graph is flipped over the x-axis (facing down) so there's a negative sign in front of the function. It's shifted to the left 4 units so it'll be |x+4|. Finally, it's shifted up 3 units so it'll be +3 outside of the absolute bracket.
NOTE: if there's a change to the x value then it's inside the bracket or parenthesis, if there's a change to the y value then it's outside of the bracket or parenthesis
Socket wrenches are on sale at 30% off the listed price is $45,what is the final cost
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{30\% of 45}}{\left( \cfrac{30}{100} \right)45}\implies 13.5~\hfill \underset{final~cost}{\stackrel{45~~ - ~~13.5}{31.5}}[/tex]
Joe is a carpenter and needs a ladder long enough to reach to a second story window that is 17 ft. from the ground. If he sets the ladder three feet from the base of the building, to the nearest tenth of a foot, how tall must the ladder be in order to reach the frame of the window? Explain your answer.
triangle - left side 17 feel, bottom 3 feet, right side - ladder
A- 17.3 ft
B- 16.7 ft
C- 20 ft
D- 25 ft
Pls Answer If you dont know the answer then dont answer or i will report
The angle of depression of the airplane is 39.8°, length of the runway is 45794 ft, and approximate height of the tower is 321 m.
What is the angle of depression of the airplane?The angle of depression of the airplane is given as follows:
Let the angle of depression be A.
[tex]A= {tan}^{ - 1} ( \frac{15000}{8000} ) = {39.8}^{o} [/tex]
Angle of depression is 39.8°.
If the angle of elevation is 6.8°, the length of the runway l is calculated thus:
horizontal distance of airplane from end of runway = d
length of runway, L = d - 80000 ft
[tex]d = \frac{15000}{tan 6.8°} = 125794 ft[/tex]
L = 125794 - 80000
L = 45794 ft
The length of the runway is 45794 ft
2. Let the height of the tower be H
[tex]H = \tan(69.8) \times 118 = 321m[/tex]
The approximate height of the tower is 321 m
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12. If angles of measures (x - 2)° and (2x + 5)° are a pair of complementary angles, find the measures of
those angles.
A) 57" and 123
O B) 27" and 63
OC) 50 and 40°
OD) 30 and 60
Answer: B
Step-by-step explanation:
The angles add to 90 degrees if they are complementary, so:
[tex]x-2+2x+5=90\\3x+3=90\\3x=87\\x=29[/tex]
So, the angles measure 29-2=27 degrees and 2(29)+5=63 degrees.
solve the system of equations y=5x-1 y=9x-9
Answer:
Look at the equations:
y
=
−
9
x
−
21
and
y
=
5
x
+
7
Because both equations equal (y), they both equal the same.
If an equations says "
y
=
−
9
x
−
21
" , that means we can replace (y) with
−
9
x
−
21
.
Therefore when i take the equation:
y
=
5
x
+
7
, we can replace (y) to get:
−
9
x
−
21
=
5
x
+
7
Now isolate (x):
−
9
x
−
21
=
5
x
+
7
⇔
−
21
=
14
x
+
7
⇔
−
28
=
14
x
⇔
x
=
−
2
Multiply:
(5x−1)(5x+4)
Answer: 25x^2+15x-4
Step-by-step explanation:
Multply 5x by the other 5x
25x^2
Multiply 5x by 4
20x
Multiply -1 by 5x
-5x
Multiply -1 by 4
-4
Add them together
25x^2+20x-5x-4
Combine like terms
20x-5x=15x
25x^2+15x-4
A circle has a radius of 18 ft. Find the length s of the arc intercepted by a central angle of 1.1 radians.
Do not round any intermediate computations, and round your answer to the nearest tenth.
The length of the arc of the circle will be 19.8 ft.
What is an arc of the circle?The arc of the circle is the distance of the circumference of the circle formed sector of the circle at a particular angle.
The formula for the length of the arc of the circle will be given as:-
Arc = Angle x radius
We have Angle = 1.1 radians Radius = 18ft
Arc = 1.1 x 18
Arc = 19.8 ft.
Therefore the length of the arc of the circle will be 19.8 ft.
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Which number line represents the solution set for the inequality -4(x + 3) ≤-2-2x?
++
-7 -6 -5 -4 -3 -2 -1 0 1 2 3
4
5 6 7
O
-7 -6 -5 -4 -3 -2 -1 0 1 2 3
4 5 6 7
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
-7 -6 -5 -4 -3 -2 -1 0 1
2
3
4
6 7
ليا
نی
für
fe
LO
5
Answer:
x<_-5
Step-by-step explanation:
-4(x+3)<_-2-2x
-4x-12<_-2-2x
-4x+2x<_-2+12
-2x<_10
-2x/-2<_10/-2
x<_-5
Instructions
Choose the best answer. If necessary, use the paper you were given.
Question
Last month Simon repaired 45 refrigerators at the Ace Appliance
Company. This month he repaired 20 percent more refrigerators than
last month. How many refrigerators did he repair this month?
Answer:
54 refrigerators
Step-by-step explanation:
In order to find the amount of refrigerators this month, we can do it in one of 2 ways.
The easier way is to multiply 45 by 1.20:
(45)(1.20) = 54
1.20 represents a 120%. This is because 45 refrigerators is 100% of last month, and Simon repaired 20% more, so 100 + 20 = 120.
The next way would be to multiply 45 by 0.20, and then add it to 45.
(45)(0.20) = 9
45 + 9 = 54
Both of the ways result in 54. So, Simon repaired 54 refrigerators this month.
Hope this helps! If you have any questions about my work, please let me know in the comments below!
helppp me thank youu!
BRAINIEST GIVEN!!
Answer:
2?
Step-by-step explanation:
2 is the square root of 4 since 2×2=4
Answer:
2
4
Step-by-step explanation:
Because 2 × 2 = 4, we know that 2 is the square root of 4.
√4 = 2
write 2(3x+5)+4(2x-1) in the form of a(bx+c)
The equivalent expression of 2(3x+5)+4(2x-1) is 2(7x + 3)
How to rewrite the expression?The expression is given as:
2(3x+5)+4(2x-1)
Open the brackets
6x + 10 + 8x - 4
Evaluate the like terms
14x + 6
Factor out 2
2(7x + 3)
Hence, the equivalent expression of 2(3x+5)+4(2x-1) is 2(7x + 3)
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D^2=290^2+2030^2
How Do i simplify this
Answer:
Step-by-step explanation:
D²=290²+2030²
=290²+(290×7)²
=290²+290²×7²
=290²(1+7²)
=290²(1+49)
=290²×50
=290²×25×2
=290²×5²×2
D=290×5×√2
D=1450√2
Which is the best estimate of the distance between the point (-25, 10) and the origin?
O 8 units
O 15 units
O23 units
O 27 units
(Please answer!)
Answer:
27 Units
Step-by-step explanation:
To find the distance using x and y components, use the Pythagorean theory [tex]a^2 + b^2 = c^2[/tex]. Set a as your x-coordinate and b as your y-coordinate (although you can flip them if you so desire). The result will you the square of your distance, so take the square root.
Alternatively, we can solve for C and find that [tex]c = \sqrt{a^2 + b^2}[/tex] or in this case [tex]distance = \sqrt{-25^2 + 10^2}[/tex].
This shows us that distance = 26.93 which is close enough to 27.
For more information: https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-pythagorean-theorem/v/the-pythagorean-theorem
if y=4 when x= -4, find y when x=7
Answer:
Answer:y=-7
Step-by-step explanation:
When x=-4 then y=4 and if x=7 then y=-7
Because y=-x
Use the strategy to simplify 4√576
Write the prime factorization of the radicand.
[tex]\begin{array}{r|l}576&2\\288&2\\144&2\\72&2\\36&2\\18&2\\9&3\\3&3\\1\end{array}[/tex]
[tex]576=2^6\cdot3^2[/tex]
Therefore
[tex]4\sqrt{576}=4\sqrt{2^6\cdot3^2}[/tex]
solve for x in the diagram below
Find the volume of the figure. Round your answer to the nearest tenth if necessary. Use 3.14 for .
A cylinder has a radius of 7 meters and a height of 2 meters.
The volume of the cylinder is approximately
m³.
help FAST!!
Answer:
[tex] \boxed{\rm \: Volume_{(Cylinder)} \approx \: 307.7 \: m {}^{3} } ( \rm \: nearest \: tenth )[/tex]
Step-by-step explanation:
Given:
radius = 7 metresheight = 2 metresπ = 3.14To Find:
Volume of the cylinderSolution:
Use the formulae of the volume of cylinder:
[tex] \boxed{\rm \: Volume_{(Cylinder)} = \pi{r} {}^{2} h}[/tex]
where,
π = 3.14r = radiush = heightAccording to the question:
radius = 7 metresheight = 2 metresSubstitute the values onto the formulae in order to find out the volume:
[tex] \rm \: Volume_{(Cylinder)} = \pi(7) {}^{2} (2)[/tex]
[tex] \rm \: Volume_{(Cylinder)} = \pi(49)(2)[/tex]
[tex]\rm \: Volume_{(Cylinder)} = 98\pi[/tex]
[tex]\rm \: Volume_{(Cylinder)} = \: 98 \times 3.14[/tex]
[tex]\rm \: Volume_{(Cylinder)} = 307.72 \: m {}^{3} \: (exact \: form)[/tex]
[tex] \boxed{\rm \: Volume_{(Cylinder)} \approx \: 307.7 \: m {}^{3} } \: ( \rm nearest \: tenth )[/tex]
Hence,we can conclude that:
The volume of the cylinder is approximately
307.7m³.
If sine of the quantity x plus y end quantity equals one half times sine of x plus radical 3 over 2 times cosine of x. What is the value of y?
A. pi over 2
B. pi over 3
C. pi over 4
D. pi over 6
The value of y from the given trig expression is pi/3 rad
Trigonometry identityThese identities are expressed in terms of sine, cosine and tangent
Given the expression
[tex]sin(x+y)=\frac{1}{2}sinx+\frac{\sqrt{3}}{2} cosx[/tex]
Expand sin(x+y)
sin(x+y) = sinxcosy + cosxsiny
Compare both equations
cosy = 1/2
y = arccos(1/2)
y = 60 degrees
y = pi/3 rad
Hence the value of y from the given trig expression is pi/3 rad
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Answer:
The answer is pi/4
When you input all the other values into the equation, they aren't true. When you input pi/4 the equation is true.
12. Find the value of x.
HELP PLS HELP
Answer:
x = 16
Step-by-step explanation:
SR = ST ⇒ Two sides are equal. So, ΔSRT is an isosceles triangle.
The angles opposite to equal sides are equal.
⇒ ∠STR = ∠R
∠STR = 4x - 28
Linear pair: If a ray stands on a line, then the adjacent angles are supplementary and they are called linear pair
∠STR + ∠STU = 180° {linear pair}
4x - 28 + 9x = 180
4x + 9x - 28 = 180 {Combine like terms}
13x- 28 = 180
Add 28 to both the sides
13x = 180 + 28
13x = 208
Divide both sides by 13
x = 208/13
[tex]\sf \boxed{x = 16}[/tex]
Answer:
x = 16
Step-by-step explanation:
since SR = ST , then Δ RST is isosceles with the 2 base angles congruent.
∠ STR = ∠ SRT = 4x - 28
∠ STR and ∠ STU are a linear pair and sum to 180° , that is
9x + 4x - 28 = 180
13x - 28 = 180 ( add 28 to both sides )
13x = 208 ( divide both sides by 13 )
x = 16
How many points marked on this graph are solutions?
Answer:
2 points are solutions
Step-by-step explanation:
A solution is a value that makes the equation true, meaning the points fall on the line. For example, the point (0,1) is on the line, which means that for the equation, when x=0, y=1. This also applies for a second point, which is about (-3.5,-1.5).
Hope this helps! :)
write the function for the graph. a. f(x) = 4 • (12)x b. f(x) = 3 • (4)x c. f(x) = 4 • (3)x d. f(x) = 3 • (12)x
The function of the graph is y = 4(3)^x
How to determine the function of the graph?The graph is an exponential function with the following points
(x,y)= (0,4) and (1,12)
An exponential function is represented as:
y = ab^x
Substitute (0,4) in the equation
4 = a * b^0
a = 4
Substitute a = 4 in y = ab^x
y = 4b^x
Substitute (1,12) in the equation
12 = 4b^1
12 = 4b
Divide by 4
b = 3
Substitute b = 3 in y = 4b^x
y = 4(3)^x
Hence, the function of the graph is y = 4(3)^x
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Find the value of (1/2)^3 A. 1/6 B. 3/6 C. 1/8 D. 1/2
Answer:
I think it's letter C.
Step-by-step explanation:
not sure correct me if I'm wrong.
We are going to multiply the fraction 1/2, to the power of 3.
This means that:
1 will be multiplied 3 times.2 will multiply 3 timesTherefore:
[tex]\bf{\left(\dfrac{1}{2}\right)^{3}=\dfrac{1\times1\times1}{2\times2\times2}=\dfrac{1}{8} }[/tex]
Therefore, the answer of the fraction (1/2)^3, is equal to 1/8.
The correct option is C.[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]
The ratio of the one leg of the right triangle to the other leg of the right triangle must be 8:7. Determine the greatest length of one leg of the right triangle given the other leg of the right triangle is 10.5 feet.
Answer:
534
Step-by-step explanation:
If f(x)=2x²+x-2, then f(-2)
Answer:
f(-2)=4
Step-by-step explanation:
put -2 where x is
f(x)=2x²+x-2
f(-2)=2(-2)²+(-2)-2
f(-2)=(2*4)-4
f(-2)=8-4
f(-2)=4
The shaded shape is a square. What are the coordinates of A and B?
the length of the bottom side is 17-3 = 10
to be a square all sides need to be 10 units.
A(7,13)
B (17,13)
5. Use an inequality symbol (<, >,=, S) to compare -3 +7-10-2
A. >
B.<
C. ≤
D. =
If the question should read as the following, then I hope my answer will help; -3 +7 _ -10 - 2
Answer: A. >
Step-by-step explanation:
Given:
-3 + 7 _ -10 - 2
Simplify both sides by combining like terms:
4 _ -12
Compare, knowing that 4 is greater than -12:
4 _ -12
4 > -12
A. >
What is the output of this program?
numA = 2
numB = 3
if numA == 2 and numB == 2:
print("yes")
elif numA == 2 and numB == 3:
print("no")
Output:
PLEASE HELP ME!!!!!!!!!
it will print no, because B = 3 and not 2 so it will skip the print yes line.