Answer:
13/4
Step-by-step explanation:
Subtract 2 from both sides. Now we have 4x=13. Divide by 4. We have our answer: x=13/4.
Solve this problem:
5X +8 = 53
5X + 8 = 53
5X = 53 - 8
X = 45 / 5
X = 9
Answer:
X=9
Step-by-step explanation:
5X+8=53
To solve this we need to make X the subject of the equation that means X should be alone on one side of the equation. Taking the following steps
5X=53-8
5X=45
X=45/5
X=9
Find the distance of the point (4,4,−4) from the line r(t)=⟨−1+2t,1+2t,3−3t⟩.
Translate the given point and line together so that you get a new point and a new line that passes through the origin. This turns the problem into finding the distance between the new point,
p = (4, 4, -4) - (-1, 1, 3) = (5, 3, -7)
and the new line,
r*(t) = r(t) - ⟨-1, 1, 3⟩ = ⟨2t, 2t, -3t⟩
Let p = ⟨5, 3, -7⟩, the vector starting at the origin and pointing to p. Then the quantity ||p - r*(t)|| is the distance from the point p to the line r*(t).
Let u be such that ||p - r*(t)|| is minimized. At the value t = u, the vector p - r*(t) is orthogonal to the line r*(t), so that
(p - r*(u) ) • r*(u) = 0
I've attached a sketch with all these elements in case this description is confusing. (The red dashed line is meant to be perpendicular to r*(t).)
Solve this equation for u :
p • r*(u) - r*(u) • r*(u) = 0
p • r*(u) = r*(u) • r*(u)
and x • x = ||x||² for any vector x, so
p • r*(u) = ||r*(u)||²
⟨5, 3, -7⟩ • ⟨2u, 2u, -3u⟩ = (2u)² + (2u)² + (-3u)²
10u + 6u + 21u = 4u ² + 4u ² + 9u ²
17u ² - 37u = 0
u (17u - 37) = 0
==> u = 0 or u = 37/17
We ignore u = 0, since the dot product of any vector with the zero vector is 0.
Then the minimum distance distance between the given point and line is
||p - r*(u)|| = ||⟨5, 3, -7⟩ - 37/17 ⟨2, 2, -3⟩|| = √(42/17)
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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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.
[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
Greatest to least just need some help will help ty(please don’t give wrong answer)
Answer:
try 91.78, 91.58, 91.26, 363.4
Step-by-step explanation:
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
The graph of a linear function is given below. What is the zero of the function?
Answer:
Need to see the problem, but the "zero of the function" is the x value when y=0.
Substitute '0' for y.
Solve for x
Answer: D
Step-by-step explanation:
convert the following to decimal fractions 99 by 5
Answer:
divide 99 by 5
99/5= 19.8
find the surface area of the prism HURRY
Answer:
Does the answer help you?
Question 24 plz show ALL STEPS
9514 1404 393
Answer:
see attached
Step-by-step explanation:
a) The first 5 partial sums are listed in the table in the attachment.
__
b) Sigma notation makes use of the general term shown:
[tex]\displaystyle\sum_{n=1}^\infty{\frac{3^n+(-2)^n}{6^n}}[/tex]
__
c) The sum appears to be close to 3/4. (For large n, a calculator cannot evaluate the terms of the series--they are too small.) The attachment shows the 100th sum to be rounded to 3/4 (from 12 significant digits).
I need help ASAP please and thank you
9514 1404 393
Answer:
C. 4 +√(x+5)
Step-by-step explanation:
The sign between the terms changes to form the conjugate. The radical contents are unchanged.
The conjugate of 4 -√(x+5) is 4 +√(x+5).
_____
Additional comment
The utility of a conjugate is that the product of a number and its conjugate is the difference of two squares. The squares are intended to remove an undesirable feature of the number, its imaginary part or its irrational part, for example. Here, the product of the number and its conjugate would be ...
(a -b)(a +b) = a² -b²
4² -(√(x+5))² = 16 -(x +5) = 11 -x . . . . no longer contains a root
a day? 6. If 18 pumps can raise 2150 tonnes of water in 50 days, working 8 hours a day, how much water will be raised in 60 days by 16 out of which 10 are working 9 hours a day and the rest 7 hours a day?
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]
Solve for
x
Round to the nearest tenth, if necessary.
9514 1404 393
Answer:
x = 5.0
Step-by-step explanation:
The tangent relation is helpful:
Tan = Opposite/Adjacent
tan(50°) = x/4.2
x = 4.2·tan(50°) ≈ 5.0054 . . . . multiply by 4.2
x ≈ 5.0
A plot of land in the shape of a horizontal ellipse has a pole at each focus. The foci are 16 feet from the center. If the plot of land is 40 feet across one axis, how long is it across the other axis?
a. 34 feet
b. 46 feet
c. 24 feet
d. 30 feet
Answer: 24 feet
Step-by-step explanation: i just guessed it on pluto and got it right. please leave a like if it worked
The length of another axis for the given ellipse will be around 25.6125 feet so none of the options will be correct.
What is an ellipse?a regular oval form produced when a cone is cut by an oblique plane that does not intersect the base, or when a point moves in a plane so that the sum of its distances from two other points remains constant.
In another word, an ellipse is a curve that becomes by a point moving in such a way that the sum of its distances from two fixed points is a closed planar curve produced.
General equation of an ellipse
(x 2 / a 2 )+ (y2 / b 2 )= 1
Given that
the plot of land is 40 feet across one axis
so 2a = 40 feet
a = 20 feet
The foci are 16 feet from the center so
c = 16
Now we know that
c = √(b² - a²)
c² = b² - a²
16² = b² - 20²
b = 25.6125
So, the length of the minor axis will be around 25.6125 feet.
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A team wishes to purchase 10 shirts of the same color. A store sells shirts in 3 different colors. What must the inventory of the store be in order to conclude that there are at least 10 shirts in one of the three colors?
Answer:
30
Step-by-step explanation:
A certain freezing process requires that room temperature be lowered from 35oC at the rate of 6oC every hour. What will be the room temperature 8 hours after the process begins?
Answer:
-13 degrees celcius.
Step-by-step explanation:
6 degrees are lowered every hour. 6*8 = 48 degrees, 48 degrees are lowered.
35-48 is -13. The room temperature will be -13 eight hours after the process begins.
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]
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)
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
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 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
1% defective parts. 100,00 parts made in total. The number of defects made should equal?
Answer:
1,000 defects
Step-by-step explanation:
Find how many defects that should be made by finding 1% of 100,000:
100,000(0.01)
= 1000
So, there should be 1,000 defects
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
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
Find the area of the triangle with vertices (0,0,0),(−4,1,−2), and (−4,2,−3).
Answer:
0.5*sqrt33
Step-by-step explanation:
A(0,0,0) B(-4,1,-2), c(-4,2,-3)
Vector AB is (-4-0,-1-0, -2-0)= (-4,-1,-2) The modul of AB is sqrt (4squared+
+(-1) squared+ (-2) squared)= sqrt (16+1+4)=sqrt21
Vector AC is (-4,2,-3) The modul of vector AC is equal to sqrt ((-4)squared+ 2squared+(-3)squared)= sqrt(16+4+9)= sqrt29
Vector BC is equal to (-4-(-4), 2-1, -3-(-2))= (0,1,-1)
The modul of BC is sqrt (1^2+(-1)^2)=sqrt2
Find the angle B
Ac^2= BC^2+AB^2-2*BC*AB*cosB
29= 2+21-2*sqrt2*sqrt21*cosB
29= 2+21-2*sqrt42*cosB
cosB= -3/ sqrt42
sinB= sqrt( 1-(-3/sqrt42)^2)=sqrt33/42= sqrt11/14
s=1/2* (sqrt2*sqrt21*sqrt11/14)=1/2*sqrt(42*11/14)= 0.5*sqrt33
You measure 49 turtles' weights, and find they have a mean weight of 80 ounces. Assume the population standard deviation is 6.1 ounces. Based on this, construct a 99% confidence interval for the true population mean turtle weight. Round your answers to 2 decimal places.
Answer:
The 99% confidence interval for the true population mean turtle weight is between 77.76 and 82.24 ounces.
Step-by-step explanation:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.575\frac{6.1}{\sqrt{49}} = 2.24[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 80 - 2.24 = 77.76 ounces.
The upper end of the interval is the sample mean added to M. So it is 80 + 2.24 = 82.24 ounces.
The 99% confidence interval for the true population mean turtle weight is between 77.76 and 82.24 ounces.
Use differentials to estimate the amount of paint needed to apply a coat of paint 0.07 cm thick to a hemispherical dome with diameter 50 m. (Round your answer to two decimal places.)
Answer:
2.75 m²
Step-by-step explanation:
From the information given:
the thickness of the paint = 0.07 cm = (0.07/100) m
= 0.0007 m thick
the diameter hemispherical dome = 50 m
∴
radius of the dome = 50m /2 = 25 m
The volume of a hemispherical dome is expressed as:
[tex]V = \dfrac{2}{3}\pi r^3[/tex]
Thus, the change in the volume now is:
[tex]\dfrac{dV}{dr} = \dfrac{2}{3}\pi *3 r^2[/tex]
[tex]{dV} = \dfrac{2}{3}\pi *3 r^2 (dr)[/tex]
[tex]{dV} = 2 \pi r^2 (dr)[/tex]
∴
dV = 2π × (25)² (0.0007)
where;
dr = 0.0007
dV = 2π × (25)² (0.0007)
dV = 2.75 m²
please help me
find x
9514 1404 393
Answer:
x = 6√2
Step-by-step explanation:
The side ratios in an isosceles right triangle are ...
1 : 1 : √2
These will be the same as ...
x : x : 12
so, ...
x = 12/√2
x = 6√2
