Answer:
Hello,
This sequence is geometric with a ratio of -3
the first term is 6
Step-by-step explanation:
[tex]u_1=6\\u_2=-18=6*(-3)=u_1*(-3)\\u_3=54=-18*(-3)=u_2*(-3)=u_1*(-3)^2\\u_4=-162=u_3*(-3)=u_1*(-3)^3\\\\...\\u_{n+1}=u_1*(-3)^n\\\\\displaystyle \sum\limits^\infty _{i=1}u_i = \lim_{n \to \infty} \sum\limits^n _{i=1}u_1*(-3)^{i-1}\\=6*\lim_{n \to \infty} \sum\limits^\infty _{i=1}(-3)^{i-1}\\=6*\frac{1-(-3)^n}{1-(-3)} \\=\dfrac{3}{2} *({1-(-3)^n)\\[/tex]
serie does not converge.
The gradient of a straight line passes through points (6,0) and (0,q) is -3/2. Find the value of q
Answer:
Step-by-step explanation:
gradient is essentially the slope of a straight line.
Use (y2-y1)/(x2-x1):
(q-0)/(0-6) = -3/2
q = 9
According to the Fundamental Theorem of Algebra, which polynomial function has exactly 8 roots?
PLS HELP IM TIMED
Answer:
Option (1)
Step-by-step explanation:
Fundamental theorem of Algebra states degree of the polynomial defines the number of roots of the polynomial.
8 roots means degree of the polynomial = 8
Option (1)
f(x) = (3x² - 4x - 5)(2x⁶- 5)
When we multiply (3x²) and (2x⁶),
(3x²)(2x⁶) = 6x⁸
Therefore, degree of the polynomial = 8
And number of roots = 8
Option (2)
f(x) = (3x⁴ + 2x)⁴
By solving the expression,
Leading term of the polynomial = (3x⁴)⁴
= 81x¹⁶
Therefore, degree of the polynomial = 16
And number of roots = 16
Option (3)
f(x) = (4x² - 7)³
Leading term of the polynomial = (4x²)³
= 64x⁶
Degree of the polynomial = 6
Number of roots = 6
Option (4)
f(x) = (6x⁸ - 4x⁵ - 1)(3x² - 4)
By simplifying the expression,
Leading term of the polynomial = (6x⁸)(3x²)
= 18x¹⁰
Degree of the polynomial = 10
Therefore, number of roots = 10
in this statement underlined the conclusion twice, underlined the hypothesis once, determine the truth value of the statement, and write it inverse converse and contrapositive. two angly of a triangle are equal if it is an isosceles triangle.
Answer:
Step-by-step explanation:
A motorist travels 90 miles at a rate of 20 miles per hour. If he returns the same distance at a rate of 40 miles per hour, what is the average speed for the entire trip, in miles per hour? (Pls explain throughly with your answer)
Answer:
80/3
Step-by-step explanation:
same distance is covered at different speed , avg speed= 2ab/a+b
= 2*20*40/60
= 80/3
Answer:
[tex]\frac{80}{3}\text{ mph}[/tex]
Step-by-step explanation:
We can use the formula [tex]d=rt[/tex] (distance = rate * time) to solve this problem.
If the motorist is travelling 90 miles to and back on a trip, he has travelled [tex]90+90=180[/tex] miles total. This represents [tex]d[/tex] in our formula.
Now we need to find the total time.
On the first trip, it's given that the motorist travels at a rate of 20 mph. Therefore, the time this trip took to travel 90 miles is:
[tex]90=20t,\\t=\frac{90}{20}=\frac{9}{2}=4.5[/tex] hours
On the second trip back, he travels the same distance (90 miles) at a rate of 40 mph. Therefore, the time the trip took is:
[tex]90=40t,\\t=\frac{90}{40}=\frac{9}{4}=2.25[/tex] hours
Therefore, the total time is [tex]4.5+2.25=6.75[/tex] hours.
Now can calculate the average speed of the entire trip:
[tex]180=6.75r,\\r=\frac{180}{6.75}=\frac{180}{\frac{27}{4}}=180\cdot \frac{4}{27}=\boxed{\frac{80}{3}\text{ mph}}[/tex]
The expected value of X, E(X) must never be less than zero. True or False.
Answer:
I think true
Step-by-step explanation:
like and mark brainlist
Select the correct answer.
The Richter scale measures the magnitude, M, of an earthquake as a function of its intensity, I, and the intensity of a reference earthquake,
M= log (I/I)
.Which equation calculates the magnitude of an earthquake with an intensity 10,000 times that of the reference earthquake?
Answer:
[tex]M = \log(10000)[/tex]
Step-by-step explanation:
Given
[tex]M = \log(\frac{I}{I_o})[/tex]
[tex]I = 10000I_o[/tex] ---- intensity is 10000 times reference earthquake
Required
The resulting equation
We have:
[tex]M = \log(\frac{I}{I_o})[/tex]
Substitute the right values
[tex]M = \log(\frac{10000I_o}{I_o})[/tex]
[tex]M = \log(10000)[/tex]
The equation that calculates the magnitude of an earthquake with an intensity 10,000 times that of the reference earthquake is A. M = ㏒10000
Since the magnitude of an earthquake on the Richter sscale is M = ㏒(I/I₀) where
I = intensity of eartquake and I₀ = reference earthquake intensity.Since we require the magnitude when the intensity is 10,000 times the reference intensity, we have that I = 10000I₀.
Magnitude of earthquakeSo, substituting these into the equation for M, we have
M = ㏒(I/I₀)
M = ㏒(10000I₀./I₀)
M = ㏒10000
So, the equation that calculates the magnitude of an earthquake with an intensity 10,000 times that of the reference earthquake is A. M = ㏒10000
Learn more about magnitude of an earthquake here:
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3/4 divided by 1/2 please hurry !!
Answer:
3/2 or 1.5
Step-by-step explanation:
(3/4) / (1/2) = (3/4) * (2/1)
= 6/4
= 3/2
It is given that,
→ 3/4 ÷ 1/2
We can divide the given values,
→ 3/4 ÷ 1/2
→ 3/4 × 2/1
→ 6/4
→ 3/2 (or) 1.5
Thus, 3/2 (or) 1.5 is the answer.
Hari earns Rs 4300 per month. He spends 80% from his income. How much does he save in a year? please give answer in step by step explaination
Saving percentage=100-80=20%
Saving amount:-
[tex]\\ \sf\longmapsto 4300\times 20\%[/tex]
[tex]\\ \sf\longmapsto 4300\times \dfrac{20}{100}[/tex]
[tex]\\ \sf\longmapsto 43\times 20[/tex]
[tex]\\ \sf\longmapsto 860[/tex]
saving per year=Saving per month×12[tex]\\ \sf\longmapsto 12\times 860[/tex]
[tex]\\ \sf\longmapsto Rs10320[/tex]
Step-by-step explanation:
i think this will be help you
I need help with this
Answer: 13.5 Okay! Here's the method count the legs of the right triangle
The formula we'll use will be
A^2 + B^2 = C^2
In this case we're counting by twos
The base is 11 so we times it by itself =110
The leg is 8.5 so we going to times itself to make 72.25 add those together so 110+ 72.25 = 182.25 then we \|-----
182.25
Then you have got ur answer of 13.5
Step-by-step explanation:
What are the coordinates A’ after 90 counterclockwise rotation about the origin.
Answer:
the above is the answer
hope this is helpful
PLS HELP!
If f(x)= x+3/4 what is the equation for f–1(x)?
A) f–1(x) = 4(x + 3)
B) f–1(x) = 4x - 3
C) f–1(x) = 4(x - 3)
D) f–1(x) = 4x + 3
Answer:
f^-1(x) = 4x-3
Step-by-step explanation:
f(x) = (x+3)/4
y = (x+3)/4
Exchange x and y
x = (y+3)/4
Solve for y
4x = y+3
Subtract 3
4x-3 = y
The inverse
f^-1(x) = 4x-3
-Ba+9=Q²a solve for a
Answer:
[tex]a= \frac{9}{B+Q^2}[/tex]
Step-by-step explanation:
Given;
-Ba+9=Q²a
To solve for "a", make "a" the subject of the formula.
First, collect similar terms together;
-Ba - Q²a = -9
multiply through by "-1" to remove the negative sign;
Ba + Q²a = 9
factor out a;
a(B + Q²) = 9
divide both sides of the equation by "(B + Q²) ";
[tex]\frac{a(B+Q^2)}{B+Q^2} = \frac{9}{B+Q^2} \\\\a = \frac{9}{B+Q^2}[/tex]
Therefore, the value of "a" in the given expression is [tex]\frac{9}{B+Q^2}[/tex]
Look at the number 45,962. Write a new
number that has the digit 4 with a value 10 times
greater than the value of the 4 in 45,962. Explain how
you determined your new number.
I'm not sure about this one..
If ABCDE is reflected over the x-axis and then translated 3 units left, what are
the new coordinates C?
Answer:
B (-2,2)
Step-by-step explanation:
Point C starts at (1,-2).
Reflect over the x axis: Point C becomes (1,2)
Translate 3 units left: Subtract 3 from x to make Point C (-2,2)
The new coordinates of C is (-2,2).
option (B) is correct.
It is required to find the new co-ordinate of C.
What is called co ordinate?Coordinates are distances or angles, represented by numbers, that uniquely identify points on surfaces of two dimensions (2D) or in space of three dimensions ( 3D ).
In the given figure ABCDE is reflected over X-axis and then translated 3 units left.
So, Point C starts at (1,-2).
Reflect over the x axis: Point C becomes (1,2).
Finally Reflect over the x axis: Point C becomes (-2,2).
OR
Translate 3 units left: Subtract 3 from x to make Point C IS (-2,2).
Thus, the new coordinates of C is (-2,2).
Learn more about the co-ordinates here:
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HELP FAST PLEASE!!!!!! Name the marked angle in 2 different ways.
Answer:
you forgot to add an image I dont know what angles your talking about
Obtain all other zeros of 2 x power 4 - 6 x cube + 3 X square + 3 x minus 2 if two of its zeros are 1\ square root 2 and -1\square root 2
Solve the following formula for the specified variable:
C = 1/2 e * p for e
Given:
The formula is:
[tex]C=\dfrac{1}{2}e\cdot p[/tex]
To find:
The formula for e.
Solution:
We have,
[tex]C=\dfrac{1}{2}e\cdot p[/tex]
Multiply both sides by 2.
[tex]2C=e\cdot p[/tex]
Divide both sides by p.
[tex]\dfrac{2C}{p}=\dfrac{e\cdot p}{p}[/tex]
[tex]\dfrac{2C}{p}=e[/tex]
Interchange the sides.
[tex]e=\dfrac{2C}{p}[/tex]
Therefore, the required formula for e is [tex]e=\dfrac{2C}{p}[/tex].
Absolute Value Equations
Answer:
4 is E, 5 is A
Step-by-step explanation:
4) Divide both sides by 5 to get |2x + 1| = 11, then solve for x to get 5 and -6.
5) Add 7 to both sides to get ½|4x - 8| = 10. Multiply both sides by 2 to get |4x - 8| = 20, then solve for x to get 7 and -3.
Which of these is a factor in this expression?
7z4 – 5 + 10 (y3 + 2)
A. -5 + 10 (y + 2)
B. (y3 + 2)
C. 7z4 – 5
D. 10 (y3 + 2)
Answer:
A
Step-by-step explanation:
-5+10(y+2) is a factor
The factor in the expression is (y³ + 2)
How to determine the factor in the expression?The expression is given as:
7z⁴ - 5 + 10 (y³ + 2)
The terms of the expressions are:
7z⁴ , -5 and 10 (y³ + 2)
The factors are
7 and z⁴10 and (y³ + 2)Hence, the factor in the expression is (y³ + 2)
Read more about expressions at:
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What represents the inverse of the function f(x) = 4x
Answer:
[tex]f { - 1}^{ } = \frac{x}{4} [/tex]
Step-by-step explanation:
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What would you do to isolate the variable in the equation below, using only one
step?
X + 9 = - 12
O Subtract 9 from both sides of the equation.
O Add 9 to both sides of the equation.
का
O Subtract 12 from both sides of the equation.
O Add 12 to both sides of the equation.
Answer:
O Subtract 9 from both sides of the equation.
Step-by-step explanation:
Notice that on the left hand side of the equation, you have two parts: X and 9. The variable is X, so we must do something to the 9 to remove it. Remember that we can cancel things by adding the negative of it. For example, 47+(-47)=0. Therefore, the opposite of 9 is -9. That essentially means subtracting 9.
1. What kind of special angle pair do the 2
angles make? (corresponding,
supplementary, or vertical)
Answer:
supplementary angle is whose is mesure is 180
please help!!!
find x
9514 1404 393
Answer:
x = (17/2)√2
Step-by-step explanation:
The ratios of sides of an isosceles right triangle are ...
1 : 1 : √2
In this problem, that is identical to ...
x : x : 17
That is, ...
[tex]x=\dfrac{17}{\sqrt{2}}=\boxed{\dfrac{17}{2}\sqrt{2}}\qquad\text{after rationalizing the denominator}[/tex]
In the following scenario for a hypothesis test for a population? mean, decide whether the? z-test is an appropriate method for conducting the hypothesis test. Assume that the population standard deviation is known. Preliminary data analyses reveal that the sample data contain no outliers but that the distribution of the variable under consideration is probably mildly skewed. The sample size is 70.
Choose the correct answer below.
a. The z-test is not an appropriate method, because the sample size is too small to be useful.
b. The z-test is an appropriate method, because the sample contains no outliers.
c. The z-test is an appropriate method, because the sample size is sufficiently large that the skewness of the variable does not matter.
d. The Z-test is not an appropriate method, because the sample is not a large sample and the data are highly skewed.
What is the slope of the line that goes through (-1, – 7) and (3, 9)?
Answer:
4
Step-by-step explanation:
We can find the slope using the slope formula
m = ( y2-y1)/(x2-x1)
= ( 9 - -7)/( 3 - -1)
= (9+7)/(3+1)
=16/4
= 4
Please answer this question. Will give brainiest fast
Answer: The answer is C the one you chose
Q is equidistant from the sides of TSR. Find the value of x.
T
(2x + 240°
30°
S
R
Lets do
[tex]\\ \sf\longmapsto 2x + 24 = 30 \\ \\ \sf\longmapsto 2x = 30 - 24 \\ \\ \sf\longmapsto 2x = 6 \\ \\ \sf\longmapsto x = \frac{6}{2} \\ \\ \sf\longmapsto x = 3[/tex]
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Answer:
yes
Step-by-step explanation:
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Determine the type of quadrilateral given the following coordinates. Show and explain all steps to prove your answer. A(2, 3) B(-1, 4) C(0, 2) D(-3, 3)
Answer:
The quadrilateral is a parallelogram
Step-by-step explanation:
If you plot the points on the graph it resembles the shape of a parallelogram. It prove this you need to check if the lengths are correct. The slope between point A and point B is 1/3 and the slope between point C and point D is also 1.3. The slope between point B and D is 1/2 and the slope between point A and point C is also 1/2
hope this helps
The quadrilateral is a parallelogram from the graph and the coordinates formed are parallel and the opposite sides have equal length.
What is a parallelogram?A parallelogram is a quadrilateral whose opposite sides are parallel and equal in length. The opposite angles of a parallelogram are equal. The diagonals of a parallelogram bisect each other.
For the given situation,
The coordinates are A(2, 3) B(-1, 4) C(0, 2) D(-3, 3).
The graph below shows these points on the coordinates and the points ABDC forms the parallelogram.
This can be proved by finding the distance between these points.
The formula of distance between two points is
[tex]AB=\sqrt{(x2-x1)^{2}+ (y2-y1)^{2}}[/tex]
Distance AB is
⇒ [tex]AB=\sqrt{(-1-2)^{2}+ (4-3)^{2}}[/tex]
⇒ [tex]AB=\sqrt{(-3)^{2}+ (1)^{2}}[/tex]
⇒ [tex]AB=\sqrt{9+ 1}[/tex]
⇒ [tex]AB=\sqrt{10}[/tex]
Distance BD is
⇒ [tex]BD=\sqrt{(-3+1)^{2}+ (3-4)^{2}}[/tex]
⇒ [tex]BD=\sqrt{(-2)^{2}+ (-1)^{2}}[/tex]
⇒ [tex]BD=\sqrt{4+ 1}[/tex]
⇒ [tex]BD=\sqrt{5}[/tex]
Distance DC is
⇒ [tex]DC=\sqrt{(0+3)^{2}+ (3-2)^{2}}[/tex]
⇒ [tex]DC=\sqrt{(3)^{2}+ (1)^{2}}[/tex]
⇒ [tex]DC=\sqrt{9+ 1}[/tex]
⇒ [tex]DC=\sqrt{10}[/tex]
Distance CA is
⇒ [tex]CA=\sqrt{(2-0)^{2}+ (3-2)^{2}}[/tex]
⇒ [tex]CA=\sqrt{(2)^{2}+ (1)^{2}}[/tex]
⇒ [tex]CA=\sqrt{4+ 1}[/tex]
⇒ [tex]CA=\sqrt{5}[/tex]
Thus the lengths of the opposite sides are equal, the given points forms the parallelogram.
Hence we can conclude that the quadrilateral is a parallelogram from the graph and the coordinates formed are parallel and the opposite sides have equal length.
Learn more about parallelogram here
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Refer to the picture above
Answer:
3.14
Step-by-step explanation:
First find the circumference of the circle:
[tex]2\pi r[/tex] = Circumference.
[tex]2 * \pi * 6[/tex] = [tex]12\pi[/tex]
Find the ratio of the angle in relation to the entire circle:
[tex]30^o[/tex] is what we have. So:
[tex]\frac{30^o}{360^o} = \frac{1}{12}[/tex]
Use the ratio and multiply the circumference to find the length:
[tex]12\pi * \frac{1}{12}[/tex] = [tex]\pi[/tex]
Round answer to the hundredth:
[tex]\pi = 3.14[/tex]
