If a log has no base written, you should generally (in algebra classes) assume that the base is 10
we raise 10 to the power log 57.9/c = 57.9/c
and 10 to the power 0.293 = 1.9633602768
so 57.9/c = 1.96
c = 57.9 /1.96 = 29.5
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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An insurance data scientist is researching a certain stretch of a rural highway where drivers are never pulled over. The mile markers in the solution of the following inequality determines the conclusion of his research. Solve and interpret the compound inequality, where x represents the mile marker along the highway.
Answer:
Drivers located below mile marker 47 or at mile marker 70 or above never get pulled over.
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
solve for x in the diagram below
Given the function h of x equals 8 times the cube root of x minus 6 end root plus 16, what is the x-intercept of the function?
–6
–2
2
16
The x-intercept of the function [tex]h(x) = 8 * \sqrt[3]{x - 6} + 16[/tex] is -2
How to determine the x-intercept?The equation of the function is given as:
[tex]h(x) = 8 * \sqrt[3]{x - 6} + 16[/tex]
The x intercept is the x value when h(x) = 0
So, we have:
[tex]8 * \sqrt[3]{x - 6} + 16 = 0[/tex]
Subtract 16 from both sides
[tex]8 * \sqrt[3]{x - 6} = -16[/tex]
Divide both sides by 8
[tex]\sqrt[3]{x - 6} = -2[/tex]
Take the cube of both sides
x - 6 = -8
Add 6 to both sides
x = -2
Hence, the x-intercept of the function [tex]h(x) = 8 * \sqrt[3]{x - 6} + 16[/tex] is -2
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What the answer to this question please
[tex]V=lwh=(3)\left(\frac{4}{3} \right) \left(\frac{3}{5} \right)\\\\V=3\left(\frac{12}{15} \right)\\\\V=\frac{36}{15}=\boxed{\frac{12}{5} \text{ cm}^{2}}[/tex]
A store is having a 20% off sale.The sale price of an item with price p is p-0.2p.what is an equivalent expression
Answer:
0.8p
Step-by-step explanation:
Hello!
As the questions states, 20% of p is 0.2p.
Simplifying the equation:
p - 0.2p0.8p0.8p is also 80% of p, which can be translated to 100% - 20% of p.
The equivalent expression is 0.8p.
If a cylinder has a volume of 120 cm3 and a cone has a volume of 360 cm3, is it possible that the two cones have congruent bases and congruent heights?
No, the cone and the cylinder can't have congruent heights and bases.
is it possible that the two cones have congruent bases and congruent heights?
The volume of a cylinder of radius R and height H is:
V = pi*R^2*H
And for a cone of radius R and height H is:
V = pi*R^2*H/3
So, for the same dimensions R and H, the cone has 1/3 of the volume of the cylinder.
Here, the cylinder has a volume of 120cm³ and the cone a volume of 360cm³, so the cone has 3 times the volume of the cylinder.
This means that the measures must be different, so the cone and the cylinder can't have congruent heights and bases.
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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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Simplify the expression
(2x^2y)3
Answer: Heyaa! ~
When simplifying (2x^2y)3 the answer will be... 6x²y
Step-by-step explanation:
Multiply the numbers:
2x²y · 3 6x²yHopefully this helps you! ^^
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]
Convert 2 1/8 into an improper fraction.
Answer:
17/8
Step-by-step explanation:
You must type 2* 8 and add 1. That makes 17/8
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to convert 2 1/8 into an improper fraction (a fraction whose numerator is greater than its denominator).
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Follow three easy steps! ^-^These are the steps:
Multiply the whole part (2) times the denominator (8). This gives us 16.Now, add the numerator, 1: 17. This is the numerator of the new fraction.Simplify if possible.However, we cannot simplify 17/8, so that's our answer.
Hope it helps you out! :D
Ask in comments if any queries arise.
#StudyWithBrainly
~Just a smiley person helping fellow students :)
I’m having trouble figuring out how to find the limit of this function algebraically.
Answer:
Step-by-step explanation:
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
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.
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]
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.
y
101
9
8
7
CO
6
5
4
3
2
1
A
12 3 4 5
B
6 7 8
9
10
Describe fully the single
transformation that takes
shape A to shape B.
X
Answer:
dilation by a factor of -1/2 about the center (6, 5)
(x, y) ⇒ (9 -x/2, 7.5 -b/2)
Step-by-step explanation:
Figure B is half the size of Figure A. It has been rotated, and translated. The single transformation must have all of these effects.
__
rotationThe orientation of shape B is the same as that of shape A. The small extension from the rectangle still points counterclockwise relative to the figure's center. However, it points west instead of east, signifying a rotation of 180°. The same 180° rotation can be accomplished by a reflection across a point.
dilationShape B has half the dimensions of shape A. That means it has been dilated by a factor of 1/2. The reflection across a point can be accomplished by using a negative dilation factor.
centerThe center of the dilation must reside between the two figures in order for "reflection across a point" to be accomplished. Each point on figure A must be twice as far from that center as the corresponding point on figure B.
Corresponding points are (1, 1) on figure A, and (8.5, 7) on figure B. The center of dilation divides the line between these points into the ratio 2:1. That center can be found as ...
(a, b) = (2(8.5, 7) +(1, 1))/3 = (17+1, 14+1)/3 = (6, 5)
single transformationThe single transformation that maps figure A to figure B is ...
dilation by a factor of -1/2 about the center (6, 5)
(x, y) ⇒ (9 -x/2, 7.5 -b/2)
Pls help with my math work
Check whether the following differential equation is exact or not. If not, then convert it into an exact differential equation.
[tex]2ydx+(x-sin\ y^{\frac{1}{2} } )dy =0[/tex]
The given differential equation is not exact, if we convert it to an exact one, we get:
[tex]2ydx + 2*(x - sin(y)^{1/2})*dy = 0[/tex]
Is the differential equation exact or not?A differential equation:
[tex]Ndx + Mdy = C[/tex]
Is exact only if:
[tex]\frac{dM}{dy} = \frac{dN}{dx}[/tex]
In this case, we have:
[tex]2ydx + (x - sin(y)^{1/2})*dy = 0\\\\then:\\\\N = 2y\\M = x - sin(y)^{1/2}[/tex]
If we differentiate, we will get:
[tex]\frac{dN}{dy} = 2\\\\\frac{dM}{dx} = 1[/tex]
So, to convert this to an exact differential equation, we need to add a factor 2 to N, this will give:
[tex]2ydx + 2*(x - sin(y)^{1/2})*dy = 0[/tex]
This is, in fact, an exact differential equation.
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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.
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
A fan in a baseball stadium is sitting in a seat with their eye level is a vertical distance of 350 ft above level.
A) When the fan is looking at home plate, the angle of depression is 30°. What is the horizontal distance from the fan to home plate? Round to the nearest 10th. Explain two different ways to determine this distance.
B) The same fan makes eye contact with a second fan in the stands that is seated at a lower row in the stadium. The straight-line distance between the eyes of the two fans is 300 ft and the angle of depression is 48°. What is the vertical distance between field level and the eyes of the second fan? Round to the nearest tenth.
=
An initial investment of $200 is now valued at $350. The annual interest rate is 8% compounded contir
equation 200e0.08 - 350 represents the situation, where t is the number of years the money has been i
how long has the money been invested? Use a calculator and round your answer to the nearest whole
O 5 years
O 7 years
O 19 years
O 22 years
Answer:
7 years
Step-by-step explanation:
Your equation should read = 200 * e^(.08 t) = 350
solving for t = 6.99 yrs ~~ 7 years
Compute the NPV for Project M if the appropriate cost of capital is 9 percent. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your final answer to 2 decimal places.) Project M Time: 0 1 2 3 4 5 Cash flow: −$2,400 $630 $760 $800 $880 $380 Should the project be accepted or rejected? multiple choice accepted rejected
The net present value is $305.73. The project should be accepted.
Net present valueUsing this formula
Net present value=Cashflow÷(1+Cost of capital)^ time
Let plug in the formula
Net present value=-$2,400+ ($630÷(1+.09)^1) + ($760÷(1+.09)^2) + ($800÷(1+.09)^3) + ($880 ÷(1+.09)^4) + ($380÷(1+.09)^5)
Net present value=-$2,400+ ( $630÷(1.09)^1) + ($760÷(1.09)^2) + ($800÷(1.09)^3) + ($880 ÷(1.09)^4) + ($380÷(1.09)^5)
Net present value=-$2,400+ ($630÷1.09) + ($760÷1.1881) + ($800÷1.295029) + ($880 ÷1.41158161) + ($380÷1.538639549)
Net present value=-$2,400+ $577.98+$639.68+$617.75+623.41+$246.91
Net present value=$305.73
Based on the above calculation the project should be accepted.
Therefore the NPV is $305.73.
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Represent "The product of 9 and a number y" mathematically.
Answer:
9y
Step-by-step explanation:
Mathematicaly, the product of 9 and a number "y" is:
9y
Tell whether the angles are adjacent or vertical. Then find the value of x.
Answer:
These are Vertical angles, adjacent angles are next to each other and make up a whole angle, while vertical angles are across and equal the same thing.
X = 81 because 84 and (x + 3) are the same so 84 minus 3 is 81
Hope that helps
What is the value of x? Enter your answer in the box.
Answer:
x = 25
Step-by-step explanation:
the line QC is parallel to BR
Then
x/15 = 40/24
Then
24x = 40×15
Then
24x = 600
Then
x = 600/24
Then
x = 25
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
What is the product?
(-2x-9y²)(-4x-3)
Answer:
8x^2 +6x +36xy^2+27y^2
Step-by-step explanation:
2x * 4x-2x*-3) -9y-^2(-4x)-9y^2(-3)