Answer:
D, 4√7
Step-by-step explanation:
Answer:
Step-by-step explanation:
c = 16
a = 12
b = ?
a^2 + b^2 = c^2
12^2 + b^2 = 16^2
144 + b^2 = 256
b^2 = 256 - 144
b^2 = 112
b^2 = 16 * 7
sqrt(b^2) = sqrt(16)*sqrt(7)
b = 4 * sqrt(7)
[tex]Solve. Clear fraction first.6/5 + 2/5 x = 89/30 + 7/6 x + 1/6[/tex]
Step-by-step explanation:
we have denominators 5, 6 and 30.
the smallest number that is divisible by all 3 is clearly 30.
so, we have to multiply everything by 30 to eliminate the fractions.
180/5 + 60/5 x = 89 + 210/6 x + 30/6 =
36 + 12x = 89 + 35x + 5
-58 = 23x
x = -58/23
MY NOTES Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.) f(x) = 2x2 − 4x + 3, [−1, 3
Answer:
b) [tex]c=1[/tex]
Step-by-step explanation:
From the question, we are told that:
Function
[tex]F(x)=2x^2-4x+9[/tex]
Given
Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) such that f(a) = f(b), then f′(x) = 0 for some x with a ≤ x ≤ b.
Generally, the Function above is a polynomial that can be Differentiated and it is continuous
Where
-F(x) is continuous at (-1,3)
-F(x) Can be differentiated at (-1.3)
-And F(-1)=F(3)
Therefore
F(x) has Satisfied all the Requirements for Rolle's Theorem
Differentiating F(x) we have
[tex]F'(x)=4x-4[/tex]
Equating F(c) we have
[tex]F'(c)=0[/tex]
[tex]4(c)-4=0[/tex]
Therefore
[tex]c=1[/tex]
i need help on 8-9 plss :))
Answer:
8. SU = 24
9. TU = 16√3
Step-by-step explanation:
Recall: SOH CAH TOA
8. Reference angle (θ) = 30°
Opposite = 8√3
Adjacent = SU
Apply TOA,
Tan θ = Opp/Adj
Substitute
Tan 30° = 8√3/SU
Tan 30° × SU = 8√3
SU = 8√3/Tan 30°
SU = 8√3/(1/√3) (tan 30° = 1/√3)
SU = 8√3*√3/1
SU = 8*3
SU = 24
9. Reference angle (θ) = 30°
Opposite = 8√3
Hypotenuse = TU
Apply SOH,
Sin θ = Opp/Hyp
Substitute
Sin 30° = 8√3/TU
Sin 30° × TU = 8√3
TU = 8√3/sin 30°
TU = 8√3/(½) (sin 30° = ½)
TU = 8√3 × 2/1
TU = 16√3
Which function describes this graph
Answer:
C.
Step-by-step explanation:
A P E X
What is the 11th term of this geometric sequence?: 16384, 8192, 4096, 2048
Answer:
16
Step-by-step explanation:
1) Find out r of the sequence. The first term(a1) is 16384, the second term (a2) is 8192.
8192=16384*r. r= 0.5
2) Use the rule that an=a1*r^(n-1)
a11=a1*r^10
a11= 16384*((0.5)^10)= 16384/ (2^10)=16.
there were 578 tickets sold for a basket all game. the activity cardholder's tickets cost $1.25 and the non-cardholders' tickets cost $2.00. the total amount of money collected was $880.00. how many of each kind of ticket were sold?
9514 1404 393
Answer:
non-cardholder: 210cardholder: 368Step-by-step explanation:
Let n represent the number of non-cardholder tickets sold. Then total revenue is ...
2.00n +1.25(578 -n) = 880.00
0.75n + 722.50 = 880.00
0.75n = 157.50 . . . . . . . . . . . subtract 722.50
n = 210 . . . . . . . . . . . . . . . divide by 0.75. Number of non-cardholder tickets
578 -n = 368 . . . . . number of cardholder tickets
368 cardholder and 210 non-cardholder tickets were sold.
Start with the number 2380.
Divide by 10,
The 8 will end up in the _____ place.
The 8 will end up in the "ones place".
How can we interpret the division?When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get. Division can be interpreted as equally dividing the number that is being divided into total x parts, where x is the number of parts the given number is divided.
We need to find the 8 will end up in which place
A negative divided by a negative is positive, then;
2380/ 10 = 238
Therefore, The 8 will end up in the _ ones_ place.
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The math teacher and cheerleading coach have teamed up to help the students do better on their math test. The cheer coach, using dance move names for the positioning of their arms, yells out polynomial functions with different degrees.
For each position the coach yells out, write the shape by describing the position of your left and right arm.
a1. Constant Function:
a2. Positive Linear Function:
a3. Negative Linear Function:
a4. Positive Quadratic Function:
a5. Negative Quadratic Function:
a6. Positive Cubic Function:
a7. Negative Cubic Function:
a8. Positive Quartic Function:
a9. Negative Quartic Function:
When it comes time to take the test not only do the students have to describe the shape of the polynomial function, you have to find the number of positive and negative real zeros, including complex. Use the equation below:
[tex]f(x)=x^5-3x^4-5x^3+5x^2-6x+8[/tex]
b. Identify all possible rational zeros.
c. How many possible positive real zeros are there? How many possible negative real zeros? How many possible complex zeros?
d. Graph the polynomial to approximate the zeros. What are the rational zeros? Use synthetic division to verify these are correct.
e. Write the polynomial in factor form.
f. What are the complex zeros?
Step-by-step explanation:
a1. The shape will be a vertical or horizontal line.
a2. The shape will be shaped like a diagonal line increasing as we go right.
a3. The shape will be shaped like a diagonal line decreasing as we go right.
a4. The shape will be shaped like a U facing upwards.
a5.The shape will be shaped like a U facing downwards.
a6. The shape will look like a S shape and it increases as we go right.
a7. The shape will look like a S shape and it decreases as We go right.
a8. The shape look like a W shape and it facing upwards.
a9. The shape look a W shape facing downwards.
We are given function.
[tex]x {}^{5} - 3x {}^{4} - 5x {}^{3} + 5x {}^{2} - 6x + 8[/tex]
b. We can test by the Rational Roots Test,
This means a the possible roots are
plus or minus(1,2,4,8).
c. If we apply Descrates Rule of Signs,
There are 3 possible positive roots or 1 possible positive root.There are also 1 possible negative root.There is also 1 possible complex root.d. Use Desmos to Graph the Function. Some roots are (-2,1,4).
e.
[tex](x {}^{2} + 1) (x - 1)(x - 4)(x + 2)[/tex]
f. The complex zeroes are
i and -i
Polynomial [tex]f(x) = x^{5} -3x^{4} - 5x^{3} + 5x^{2} - 6x + 8[/tex] in factor form: (x-1)(x+2)(x-4)(x-i)(x+i)
What is a polynomial?A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
Shape of the graph for the following polynomial:
Constant function - straight line parallel to x axis.Positive linear function - straight line slanting upwards from left to right.Negative linear function - straight line slanting downwards from left to right.Positive quadratic function - U shaped curve opening upwardsNegative quadratic function - U shaped curve opening downwardsPositive cubic function - right hand curved upwards, left hand curved downwards.Negative cubic function - Left hand curved upwards, right hand curved downwards. Positive quartic function - W shaped facing upwardsNegative quartic function - W shaped facing downwardsFinding zeros of the polynomial given:
[tex]f(x) = x^{5} -3x^{4} - 5x^{3} + 5x^{2} - 6x + 8[/tex]
By factor theorem, if f(t) = 0, t is a zero of the polynomial.
Taking t = 1.
f(1) = 1 - 3 - 5 + 5 - 6 + 8 = 0
(x - 1) is a factor of the polynomial f(x).
Divide f(x) by (x-1) using long division to find the other factors.
f(x)/(x-1) = [tex]x^{4} -2x^{3}-7x^{2} -2x-8[/tex] is also a factor of f(x).
Factorizing it further:
g(x) = [tex]x^{4} -2x^{3}-7x^{2} -2x-8[/tex]
g(-2) = 16 + 16 - 28 + 4 - 8 = 0
(x + 2) is a factor of g(x) and thus f(x).
g(x)/(x+2) = [tex]x^{3} - 4x^{2} +x - 4[/tex] is a factor of f(x).
Factorizing it further:
k(x) = [tex]x^{3} - 4x^{2} +x - 4[/tex]
k(4) = 64 - 64 + 4 - 4 = 0
(x - 4) is a factor of k(x) thus of f(x).
k(x)/(x-4) = [tex]x^{2} +1[/tex]
Factorizing it further:
l(x) = [tex]x^{2} +1[/tex] = (x + i)(x - i)
Zeros of f(x) = 1, -2, 4, ±i
Rational zeros : 1, -2, 4
Positive real zeros: 1, 4
Negative real zeros: -2
Complex zeros: ±i
Polynomial in factor form: (x-1)(x+2)(x-4)(x-i)(x+i).
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Round 5,821 to the nearest thousands place:
Answer:
6000 hope this helps
if the question is 5,422 then the round figure is 5000
but the question is 5,821 its above 5500 will be 6000
What is the area of a square with a side length of 32 yards?
Answer:
A=1024 yd.^2
Step-by-step explanation:
A=s^2
Substitute,
A=32^2
So,
A=1024 yd.^2
Answer:
1024 yd²
Step-by-step explanation:
Since it's a square, the side lengths will all be the same length. Due to this, you can square the given value to find the area.
A(Square) = 32² = 1024
convert the following to decimal fractions 99 by 5
Answer:
divide 99 by 5
99/5= 19.8
kabura bought a piece of cloth 3 metres long. The material shrunk by 1% after washing. What was the new length of the cloth
Answer:
2.97m
Step-by-step explanation:
1% of 3m =1/100×3=0.03
0.03m of cloth was shrunk,
So, New lenght : 3-0.03=2.97m
please help me with both questions
Answer:
(b) 829 seconds
(c) 13.8 minutes
Step-by-step explanation:
(b) 2.48×10⁸/2.99×10⁵ = 829 seconds
(c) 829/60 = 13.8 minutes
A right pyramid with a square base has
volume of 252 cubic centimeters. The
length of one of the sides of its base is 6
centimeters. Rounded to the nearest
centimeter, what is the vertical height of
the pyramid?
Hey there!
A right pyramid with a square base just means that it isn't slanted all funny. If you create a triangle with a point on one of the edges of the base, the center of the base, and the top of the pyramid, it would be a right triangle.
To find the volume of a right pyramid, you just take the base area, multiply it by the height, and then divide by three.
However, we are looking for the height. We have been given, so we will just go backwards.
252×3=756 (multiply instead of divide)
6×6=36 (base is a square, so you just square 6. This is our base area)
756/36=21
So, the vertical height of the pyramid is 21 cubic centimeters.
Have a wonderful day! :D
find the surface area of the prism HURRY
Answer:
Does the answer help you?
Determine if the described set is a subspace. Assume a, b, and c are real numbers. The subset of R3 consisting of vectors of the form [a b c] , where at most one of a , b and c is non 0.
The set is a subspace.
The set is not a subspace.
If so, give a proof. If not, explain why not.
Answer:
Not a subspace
Step-by-step explanation:
(4,0,0) and (0,4,0) are vectors in R3 with zero or one entries being nonzero, but their sum, (4,4,0) has two nonzero entries.
In an interview for a secretary position at the dealer, a typist claims a tying speed of 45 words per minute. On
On the basis of 70 trials, she demonstrated an average speed of 43 words per minute with a standard deviation of 15 words per minute.
Test at 5% significance level on the typist’s claim.
Using the hypothesis test for one sample mean, There is NO SIGNIFICANT EVIDENCE to support the typist's claim
[tex]H_{0} = 45\\H_{1} < 45\\\\[/tex]
The test statistic :
T = (x - μ) ÷ (s/√(n))
T = (43 - 45) ÷ (15/√70)
T = - 2 ÷ 1.7928429
T = -1.12
At α = 0.05
Pvalue :
Degree of freedom, df = 70 - 1 = 69
Pvalue = 0.1333
Decision region :
Reject [tex]H_{0}[/tex] if Pvalue < α
0.1333 > 0.05
Since Pvalue > α We fail to reject the Null
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What is the simplified form of the following expression? Assume x > 0.
3
2x
16x
2x
4/24x²
2x
4/2443
16x4
124²
Answer:
fourth root of 24 x cubed/16x to the power four
Consider the given statement. Determine whether its is equivalent to the given statement, a negation, or neither. Attached is the photo reference.
Answer:
1. Negation
2. Equivalent
3. Neither
4. Neither
Step-by-step explanation:
p ^ ~q
~q → p~
~q ∨ p
~p ∨q
A plane flying horizontally at an altitude of 3 mi and a speed of 460 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 4 mi away from the station (Round your answer to the nearest whole number.) 368 X mi/h Enhanced Feedback Please try again. Keep in mind that distance - (altitude)2 + (horizontal distance)? (or y = x + n ). Differentiate with respect to con both sides of the equation, using the Chain Rule, to solve for the given speed of the plane is x.
Answer:
[tex]\frac{dy}{dt}=304mi/h[/tex]
Step-by-step explanation:
From the question we are told that:
Height of Plane [tex]h=3mi[/tex]
Speed [tex]\frac{dx}{dt}=460mi/h[/tex]
Distance from station [tex]d=4mi[/tex]
Generally the equation for The Pythagoras Theorem is is mathematically given by
[tex]x^2+3^2=y^2[/tex]
For y=d
[tex]x^2+3^2=d^2[/tex]
[tex]x^2+3^2=4^2[/tex]
[tex]x=\sqrt{7}[/tex]
Therefore
[tex]x^2+3^2=y^2[/tex]
Differentiating with respect to time t we have
[tex]2x\frac{dx}{dt}=2y\frac{dy}{dt}[/tex]
[tex]\frac{dy}{dt}=\frac{x}{y}\frac{dx}{dt}[/tex]
[tex]\frac{dy}{dt}=\frac{\sqrt{7}}{4} *460[/tex]
[tex]\frac{dy}{dt}=304.2614008mi/h[/tex]
[tex]\frac{dy}{dt}=304mi/h[/tex]
Police estimate that 25% of drivers drive without their seat belts. If they stop 6 drivers at random, find theprobability that more than 4 are wearing their seat belts.
Answer:
%17.80
Step-by-step explanation:
17.8% is the probability that more than 4 are wearing their seat belts.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given that Police estimate that 25% of drivers drive without their seat belts.
If they stop 6 drivers at random we need to find the probability that more than 4 are wearing their seat belts.
For each driver stopped, there are only two possible outcomes. Either they are wearing their seatbelts, or they are not.
he drivers are chosen at random, which mean that the probability of a driver wearing their seatbelts is independent from other drivers.
Police estimate that 25% of drivers drive without their seat belts.
This means that 75% wear their seatbelts, so P=0.75
If they stop 6 drivers at random, find the probability that all of them are wearing their seat belts.
[tex]P(X=x)=C_{n,x} p^{x} (1-p)^{n-x}[/tex]
[tex]P(X=6)=C_{6,6} 0.75^{6} (1-0.75)^{0} =0.1780[/tex]
Hence, 17.8% is the probability that more than 4 are wearing their seat belts.
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Which is the answer choice to this question?
Answer:
D
Step-by-step explanation:
Graph it
Write an expression for the baseball team’s Purchase.
Helpp me plzzz im being timed
Venn diagrams: unions, intersections, and complements
Attached is the photo reference
Answer:
a) 0
b) 2,3,4,5,6,7
c)3,4,6,7
Step-by-step explanation:
If average of the numbers 3,9,5,7 and Q is 5 times the value of Q, find the value of Q
Answer:
q=6
Step-by-step explanation:
3+9+5+7+Q=5Q
5Q-Q=24
Q=6
HELP PLEASE!!!
Oak wilt is a fungal disease that infects oak trees. Scientists have discovered that a single tree in a small forest is infected with oak wilt. They determined that they can use this exponential model to predict the number of trees that will be infected after t years.
f(t)=e^0.4t
Question:
Rewrite the exponential model as a logarithmic model that calculates the # of years, g(x) for the number of infected trees to reach a value of x.
The logarithmic model is:
[tex]g(x) = \frac{\ln{x}}{0.4}[/tex]
-------------
We are given an exponential function, for the amount of infected trees f(x) after x years.To find the amount years needed for the number of infected trees to reach x, we find the inverse function, applying the natural logarithm.-------------
The original function is:
[tex]y = f(x) = e^{0.4x}[/tex]
To find the inverse function, first, we exchange y and x, so:
[tex]e^{0.4y} = x[/tex]
Now, we have to isolate y, and we start applying the natural logarithm to both sides of the equality. So
[tex]\ln{e^{0.4y}} = \ln{x}[/tex]
[tex]0.4y = \ln{x}[/tex]
[tex]y = \frac{\ln{x}}{0.4}[/tex]
Thus, the logarithmic model is:
[tex]g(x) = \frac{\ln{x}}{0.4}[/tex]
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What is the image point of (4, -6) after a translation right 5 units and up 4 units?
Answer:
(9,-2)
Step-by-step explanation:
5 is the x coordinate, and 4 is the y coordinate. When you go right a certain amount of units, you add those units to your x coordinate. If you were to go left a certain amount of units, you'd subtract them. Since we're going right, 5 + 4 = 9. When you go up a certain amount of units, you add those units to you y coordinate. If you were to go down a certain amount of units, you'd subtract them. Since we're going up, -6 + 4 = -2. So, x = 9 and y = -2, or (9,-2)
If x/4-y/6=1/6 and y/z=1/2, then what is the value of 3x-z?
A. 4
B.6
C. 3
D. 2
E. None
PLSS HELPPPP WILL GIVE BRAINLESSS A 22-foot ladder is resting against the side of a building. The bottom of the ladder is 3 feet from the building. Find the measure of the angle the ladder makes with the ground. Round your answer to the nearest tenth of a degree.
Answer:
The answer is 82.2
Step-by-step explanation
hope this helps
