Answer:
Step-by-step explanation:
this the gemetric sequence because : -12/6 =24/-12=-48/24=-2 (common rat)
the sum is : S= u1 ×(d^n - 1)(d-1)
d = -2 u1 = 6 S= -2046
6((-2)^n -1) /(-2 -1) = -2046
(-2)^n -1 =1023
(-2)^n = 1024 but 1024 = 2^10 = (-2)^10
so : (-2)^n = (-2)^10
n=10 conclusion : 10 terms
The number of terms of the sequence is 10.
What is geometric sequence?
A geometric sequence exists a sequence of numbers where each term after the first term exists found by multiplying the earlier one by a fixed non-zero number, named the common ratio.
The terms of the sequence 6, -12, 24, -48, ...
Sum = -2046
Geometric sequence:
-12/6 = 24/-12 = -48/24 = -2
Sum of terms:
[tex]$S = u_{1} *(d^n - 1)(d-1)[/tex]
Let, d = -2, [tex]u_{1} = 6[/tex] and S = -2046
[tex]6((-2)^n -1) /(-2 -1) = -2046[/tex]
[tex](-2)^n -1 =1023[/tex]
[tex](-2)^n = 1024[/tex]
But the number of terms = 10
[tex]1024 = 2^{10} = (-2)^{10}[/tex]
so,[tex](-2)^{n} = (-2)^{10}[/tex]
Therefore, the correct answer is 10.
To learn more about geometric sequence
https://brainly.com/question/1729067
#SPJ2
The graphs below are both quadratic functions. The equation of the red graph is
x)= x. Which of these is the equation of the blue graph, g(x)?
Answer:
D. [tex]g(x)=\frac{1}{5}x^2[/tex]
Step-by-step explanation:
The equation of the red quadratic graph is [tex]f(x)=x^2[/tex].This is the parent quadratic function or the base of the quadratic functions.This red quadratic graph has been dilated by a certain scale factor to obtain the blue graph. Recall that, when the scale factor is a fraction, such that [tex]0\:<\:k\:<\:1[/tex] the graph is stretched horizontally.The dilated graph then becomes wider than the parent function.From the given function equations, the possible value of k can only be [tex]k=\frac{1}{5}[/tex].Therefore the blue graph has equation: [tex]g(x)=\frac{1}{5}x^2[/tex]The correct answer is D.The factored form of polynomial P(x) shows only two of its roots. Assuming all of the
coefficients in the expanded form of P(x) are real, select each number that could be a
missing root of p(x)
Answer:
C and E
Step-by-step explanation:
Recall that according to the complex conjugate theorem, if P(x) is a polynomial function with real coefficients, and a+bi is an imaginary root of P(x), then its conjugate (i.e a-bi) must also be a root.
Here we see that 2 of the given roots are imaginary : i and 2+i
by the theorem given above, the conjugates of these must also be roots
i.e -i and 2-i
Nick found the quotient of 8.64 and 1.25....
Answer:
No, the power multiplied to 8.64 should havean exponent of zero.
HOPE THIS WILL HELP YOU
Answer:
No, The power multiplied to 8.64 should have an 0 exponent.
Option 2 is correct
Step-by-step explanation:
Nick found the quotient of 8.64 and 1.25 × 10⁵.
Quotient of two number is form of division.
If quotient of a and b then expression is [tex]\dfac{a}{b}[/tex]
Correct steps:
[tex]\Rightarrow \dfrac{8.64\times 10^0}{1.25\times 10^5}[/tex]
[tex]\Rightarrow (8.64\div1.25)\times 10^{0-5}[/tex]
[tex]\Rightarrow 6.912\times 10^{-5}[/tex]
Nick steps:
[tex]\Rightarrow \dfrac{8.64\times 10^1}{1.25\times 10^5}[/tex] wrong step
[tex]\Rightarrow (8.64\div1.25)\times 10^{1-5}[/tex]
[tex]\Rightarrow 6.912\times 10^{-4}[/tex]
The power multiplied to 8.64 should have an 0 exponent.
Therefore, Nick was wrong.
Find the first five terms of the sequence in which a1 = –10 and an = 4an – 1 + 7, if n ≥ 2.
To determine the first five terms of the given recursive sequence, we begin with the first term, a1 = -10, and use the provided recurrence relation to calculate each subsequent term. The first five terms of the sequence are -10, -33, -125, -493, and -1965.
Explanation:The student has presented a recursive sequence with the first term stated as – 10 and a recursive formula to find any subsequent term, an, defined as an = 4an-1 + 7 for n ≥ 2.
To find the first five terms of the sequence, we'll apply the formula starting with a1 and proceed to each next term.
First term, a1: – 10
Second term, a2: 4(– 10) + 7 = – 40 + 7 = – 33
Third term, a3: 4(– 33) + 7 = – 132 + 7 = – 125
Fourth term, a4: 4(– 125) + 7 = – 500 + 7 = – 493
Fifth term, a5: 4(– 493) + 7 = – 1972 + 7 = – 1965
Therefore, the first five terms of the sequence are – 10, – 33, – 125, – 493, and – 1965.
Write your answer without using negative exponents.
(w^5)^-7
Your answer would be [tex]\frac{1}{w^{35} }[/tex]
This is because (w^5)^-7 expands to give w^-35 because you multiply the exponents. When you have a negative exponent, this can also be written as a reciprocal, i.e. x^-2 = 1/x². This means that we can write w^-35 as 1/(w^35), which doesn't include any negative exponents.
I hope this helps! Let me know if you have any questions :)
The answer without using negative exponents [tex](w^{5})^{-7}[/tex] is [tex]\frac{1}{w^{35} }[/tex] .
What are the properties of exponents ?The following properties of exponents are -
[tex](a^{m})^{n}[/tex] = [tex]a^{m*n}[/tex] [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex] How to solve expression using properties of exponents ?Given expression is [tex](w^{5})^{-7}[/tex] .
Using the properties of exponents, we have -
= [tex]w^{-35}[/tex]
= [tex]\frac{1}{w^{35} }[/tex] which does not have any negative exponents.
Thus, the answer without using negative exponents [tex](w^{5})^{-7}[/tex] is [tex]\frac{1}{w^{35} }[/tex] .
To learn more about properties of exponents, refer -
https://brainly.com/question/3187898
#SPJ2
A circuit is supplied with 24 volts and its load offers a total resistance of 400 ohm. What’s the total circuit power?
Answer:
P = 1.44 Watts
Step-by-step explanation:
We know that the relation between voltage and current in a simple circuit with a resistor is
V = I.R
Where
V = the voltage of the source
I = current of the circuit
R = resistance
The power is defined as
P = V.I
Which is the same as
P = V.(V/R)
P = (24 v)^2 / (400 ohm)
P = 1.44 Watts
What’s the recipical of 7/9
Answer:
The reciprocal of [tex] \frac { 7 } { 9 } [/tex] is [tex] \frac { 9 } { 7 } [/tex].
Step-by-step explanation:
We are asked about the reciprocal of the given fraction [tex] \frac { 7 } { 9 } [/tex].
We know that in mathematics, a reciprocal is the multiplicative inverse of a number.
For example, in case of a fraction, its reciprocal will be its inverse which means that we swap the places of numerator and denominator.
So the reciprocal of [tex] \frac { 7 } { 9 } [/tex] will [tex] \frac { 9 } {7 } [/tex].
Fractions are always set up with numerator on top and denominator on bottom like so:
[tex]\frac{numerator}{denominator}[/tex]
To take the reciprocal of a number you must switch the places of numerator and denominator.
Reciprocal of [tex]\frac{7}{9}[/tex] is [tex]\frac{9}{7}[/tex]
Hope this helped!
~Just a girl in love with Shawn Mendes
When is g(x) = 0 for the function g(x) = 5.23x + 4?
Answer:
g(x)=4
Step-by-step explanation:
5.23(0)+4=4
Hope this helps!
name the property. 2(xy)=(2x)y
Answer:
associative property of multiplication
Step-by-step explanation:
If we have 3 numbers x, y and z the associative property of multiplication says that:
[tex]x (yz) = z (xy) = (xz)y[/tex]
This means that the result will be the same regardless of the order in which the multiplication takes place.
In this case we have the following equality
[tex]2(xy) = (2x)y[/tex]
Note that the property used is the associative property of multiplication
15p!!!!What is the percent of change from 56 to 22? round to the nearest percent
Answer:
60.7143% decrease or 60%
Step-by-step explanation:
The percent of change from 56 to 22 is 60%.
The percent of change from 56 to 22 is 60%.
What is problem-solving?
Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.
Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.
Learn more about Problem-solving here: brainly.com/question/13818690
#SPJ2
Solve this rational equation
Answer:
x = -1Step-by-step explanation:
[tex]\text{Domain:}\\\\x-4\neq0\ \wedge\ x-2\neq0\ \wedge\ x^2-6x+8\neq0\\\\x\neq4\ \wedge\ x\neq2\ \wedge\ x^2-4x-2x+8\neq0\\\\x\neq4\ \wedge\ x\neq2\ \wedge\ x(x-4)-2(x-4)\neq0\\\\x\neq4\ \wedge\ x\neq2\ \wedge\ (x-4)(x-2)\neq0\\\\x\neq4\ \wedge\ x\neq2\ \wedge\ x-4\neq0\ \wedge\ x-2\neq0\\\\\boxed{D:x\neq4\ \wedge\ x\neq2}[/tex]
[tex]\dfrac{1}{x-4}+\dfrac{x}{x-2}=\dfrac{2}{x^2-6x+8}\\\\\dfrac{1(x-2)}{(x-4)(x-2)}+\dfrac{x(x-4)}{(x-4)(x-2)}=\dfrac{2}{(x-4)(x-2)}\\\\\dfrac{x-2+x(x-4)}{(x-4)(x-2)}=\dfrac{2}{(x-4)(x-2)}\iff x-2+x(x-4)=2\\\\x-2+(x)(x)+(x)(-4)=2\\\\x-2+x^2-4x=2\qquad\text{subtract 2 from both sides}\\\\x^2-3x-4=0\\\\x^2-4x+x-4=0\\\\x(x-4)+1(x-4)=0\\\\(x-4)(x+1)=0\iff x-4=0\ \wedge\ x+1=0\\\\x-4=0\qquad\text{add 4 to both sides}\\x=4\notin D\\\\x+1=0\qquad\text{subtract 1 from both sides}\\x=-1\in D[/tex]
how do you factor x squared minus 100
Answer:
(x - 10)(x + 10)
Step-by-step explanation:
x² - 100 ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b)
Hence
x² - 100
= x² - 10² = (x - 10)(x + 10)
Pip and Sara win some money and share it in the ratio 5:4. Pip gets £50. How much did they win in total?
Answer:
90
Step-by-step explanation:
Write the ratio this way
Pip: Sara: Total
5 : 4 : 9
We multiply each by 10 to get Pip to 50 (5*10 = 50)
5*10: 4*10: 9*10
50 : 40 : 90
Answer:
$90
Step-by-step explanation:
Given that the ratio of Pip: Sara is 5:4
This means :
Pip gets 5 parts
Sara gets 4 parts
Together they have 5 + 4 parts = 9 parts
Also given that Pip's 5 parts is equivalent to $50
Hence each 1 part is $50/5 = $10
if 1 part = $10
The total 9 parts = 9 x $10 = $90
What is the value of k?
k = 28
k = 29
K=31
K=42
The attachment should answer some of your guys “what does k=?” Questions
The numerator and denominator of a fraction are in the ratio of 3 to 5. If the numerator and denominator are both increased by 2, the fraction is now equal to 2/3.
If n = the numerator and d = the denominator, which of the following systems of equations could be used to solve the problem?
5n = 3d and 3n + 6 = 2d + 4
5n = 3d and 4n + 4 = 3d + 6
3n = 5d and 3n + 6 = 2d + 4
Answer:
3n=5d and 3n = 5d and 3n + 6 = 2d + 4
Step-by-step explanation:
Answer: The correct option is
(A) [tex]5n=3d~~~\textup{and}~~~3n+6=2d+4.[/tex]
Step-by-step explanation: Given that the numerator and denominator of a fraction are in the ratio of 3 to 5. When the numerator and denominator are both increased by 2, the fraction is equal to \dfrac{2}{3}.
We are to select the system of equations that could be used to solve the problem.
Since n denotes the numerator and m denotes the denominator of the given fraction, so we have
[tex]\dfrac{n}{d}=\dfrac{3}{5}\\\\\\\Rightarrow 5n=3d,[/tex]
and
[tex]\dfrac{n+2}{d+2}=\dfrac{2}{3}\\\\\\\Rightarrow 3(n+2)=2(d+2)\\\\\Rightarrow 3n+6=2d+4.[/tex]
Thus, the required system of equations is
[tex]5n=3d~~~\textup{and}~~~3n+6=2d+4.[/tex]
Option (A) is CORRECT.
The graph of function f is defined as the set of all points (x, f(x)), where x is in the domain of f.
Please select the best answer from the choices provided
T
F
Answer:
True
Step-by-step explanation:
The domain of a function is the complete set of possible values of the independent variable 'x'. Therefore, the graph of funtion is defined as the set of all points (x, f(x)) where 'x' is the domain of f(x).
Hence, the statement is TRUE
Answer:
True (Please give brainliest)
Step-by-step explanation:
Write the equation of the line that has a y-value that increases by 4 for every x that increases by 1. It also crosses the y-axis at –2. A. y = 4x – 2 B. y1/4x – 2 C. y = 2x + 1/4D. y = 2x – 4
ANSWER
[tex]y = 4x - 2[/tex]
EXPLANATION
The equation of a straight line can be found using the formula
[tex]y =mx + b[/tex]
We have that,the y-value increases by 4 for every x that increases by 1.
This implies that, the slope is
[tex]m = \frac{4}{1} = 4[/tex]
The line also crosses the y-axis at –2.
Hence the y-intercept is b=-2.
Therefore the equation is
[tex]y = 4x - 2[/tex]
The correct answer is A
ABCD is a parallelogram in which in which angle a is 110. Find the measure of each of the angles b,c,d
Answer:
m < b = 70, m < c = 110 and m < d = 70 degrees.
Step-by-step explanation:
The opposite angle a ( angle c) = a = 110 degrees (Property of a parallelogram).
The angle on the same line as a ( that is angle b) = 180 - 110 = 70 degrees.
(Property of a parallelogram).
Finally angle d which is opposite angle b = 70 degrees.
Final answer:
In parallelogram ABCD with angle A being 110 degrees, angle C is also 110 degrees as opposite angles are equal. Angles B and D are 70 degrees each since consecutive angles in a parallelogram are supplementary and add up to 180 degrees.
Explanation:
To find the measures of the angles B, C, and D in the parallelogram ABCD with angle A being 110 degrees, we can use the properties of parallelograms. Specifically, opposite angles in a parallelogram are equal, and consecutive angles are supplementary (add up to 180 degrees).
Since angle A is 110 degrees, angle C, being opposite to angle A, also measures 110 degrees. Now, to find the measures of angles B and D we know that:
Angle A and angle B are consecutive, so they add up to 180 degrees. Therefore, angle B equals 180 degrees - 110 degrees which is 70 degrees.
Similarly, angle C and angle D are consecutive, so angle D also measures 180 degrees - 110 degrees, giving us 70 degrees for angle D as well.
Thus, the measures of angles B, C, and D in parallelogram ABCD are 70 degrees, 110 degrees, and 70 degrees, respectively.
The area of a triangle is 40 cm2. The height of the triangle is 4 cm. What is the measure of the base of the triangle?
A.
40 cm
B. 32 cm
C. 28 cm
D. 20 cm
Answer:
Step-by-step explanation:
Givens
Height = h = 4cm
b = ?
Area = 40 cm^2
Formula
Area = 1/2 * h * b
Solution
40 cm^2 = 1/2 * 4 * b Combine the right
40 cm^2 = 2 * b Divide by 2
40 cm^2 /2 = 2b/2 Do the division
20 cm = b
Answer D
Which is equivalent
For this case we must find an expression equivalent to:
[tex]\sqrt [5] {13 ^ 3}[/tex]
By definition of properties of powers and roots we have:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
Then, rewriting the expression:
[tex]13 ^ {\frac {3} {5}}[/tex]
Answer:
Option D
[tex]13 ^ {\frac {3} {5}}[/tex]
Solve the following equation for x: 5x + 3y = 15.
A.x = negative three fifthsy − 3
B.x = negative three fifthsy + 3
C.x = three fifthsy + 3
D.x = three fifthsy − 3
Answer:
B
Step-by-step explanation:
5x + 3y = 15
5x = -3y +15
x = -3/5y +3
Answer:
The correct option is B) x = negative three fifths y + 3
Step-by-step explanation:
Consider the provided equation.
5x + 3y = 15
We need to solve the above equation for x.
Subtract both the side by 3y.
[tex]5x + 3y-3y = 15-3y[/tex]
[tex]5x= 15-3y[/tex]
To find the value of y, isolate the variable y:
Divide both the sides by 5.
[tex]\frac{5x}{5}= \frac{15}{5}-\frac{3y}{5}[/tex]
[tex]x= 3-\frac{3y}{5}[/tex]
[tex]x= -\frac{3y}{5}+3[/tex]
Hence, the correct option is B) x = negative three fifths y + 3
which is the measure of XBA if ray BA bisects XBY, which measures 86 grades?
Answer:
∠XBA=43°
Step-by-step explanation:
we know that
If ray BA bisect angle ∠XBY
then
∠XBA=∠XBY/2
we have
∠XBY=86°
substitute
∠XBA=86°/2=43°
5x - 47< 3(12x - 108) – 2
Answer:
9 < x
Step-by-step explanation:
5x - 47< 3(12x - 108) – 2
Distribute
5x - 47< 36x - 324 – 2
Combine like terms
5x - 47< 36x-326
Subtract 5x from each side
5x-5x - 47< 36x-5x-326
- 47< 31x-326
Add 326 to each side
326 - 47< 31x-326+326
279 < 31x
Divide by 31 on each side
279/31 < 31x/31
9 < x
How do you convert 3.16 (6 repeating) to a fraction?
Suppose [tex]x=3.1\overline6[/tex]. Then [tex]10x=31.\overline6[/tex], and [tex]100x=316.\overline6[/tex].
Now,
[tex]100x-10x=316.\overline6-31.\overline6=316-31[/tex]
[tex]\implies90x=285[/tex]
[tex]\implies x=\dfrac{285}{90}=\boxed{\dfrac{19}6}[/tex]
find the solution set.
8x^2+7x-1=0
Answer:
x = - 1, x = [tex]\frac{1}{8}[/tex]
Step-by-step explanation:
Given
8x² + 7x - 1 = 0 ← in standard form
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term
product = 8 × - 1 = - 8 and sum = + 7
The factors are + 8 and - 1
Use these factors to split the x- term
8x² + 8x - x - 1 = 0 ( factor the first/second and third/fourth terms )
8x(x + 1) - 1(x + 1) = 0 ← factor out (x + 1) from each term
(x + 1)(8x - 1) = 0
Equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
8x - 1 = 0 ⇒ 8x = 1 ⇒ x = [tex]\frac{1}{8}[/tex]
Answer:
x
=
1
8
,
−
1
x=1/8,-1 I solved using the quadratic formula
Step-by-step explanation:
Which expressions are equivalent to 2 In a + 2 In b - In a? Refer to the picture for the option listed!
Which polynomial has factors of 4x – 7 and x + 4?
answer: 4x² + 9x - 28.
multiply the factors together:
4x times x = 4x²
4x times 4 = 16x
-7 times x = -7x
-7 times 4 = 28
therefore, (4x-7) times (x+4) = 4x² + 16x -7x = 28
next, you must condense and simplify your answer:
16x -7x equals 9x
your final answer should be 4x² + 9x - 28.
Answer:
The answer is B aka 4x² + 9x - 28.
Step-by-step explanation:
The turning point of the curve: y=6-4x-x^2
Answer:
The turning point is (-2,10)
Step-by-step explanation:
we have
[tex]y=6-4x-x^{2}[/tex]
This is a quadratic equation (vertical parabola) open downward
we know that
The turning point of a quadratic equation is the vertex
so
Convert the quadratic equation into vertex form
[tex]y-6=-4x-x^{2}[/tex]
[tex]y-6=-(x^{2}+4x)[/tex]
[tex]y-6-4=-(x^{2}+4x+4)[/tex]
[tex]y-10=-(x^{2}+4x+4)[/tex]
[tex]y-10=-(x+2)^{2}[/tex]
[tex]y=-(x+2)^{2}+10[/tex] ----> equation in vertex form
The vertex is the point (-2,10)
therefore
The turning point is (-2,10)
The turning point of the parabola described by the equation y=6-4x-x^2 is at the point (-2, 10), which is a maximum since the parabola opens downwards.
Explanation:To find the turning point of the curve given by the equation y=6-4x-x^2, we first need to rewrite the equation in the form of the vertex of a parabola, which is given by y=a(x-h)^2+k, where (h,k) is the coordinate of the turning point or vertex. Noting that there is a mistake in the information provided since the second derivative would actually be y" = -2, and not 6x - 12, indicating that we have a concave down parabola with a maximum point, not a point of inflection. We can complete the square to rewrite the function in vertex form.
Start by completing the square: y = -x^2 - 4x + 6 can be rewritten as y = -(x^2 + 4x) + 6. Adding and subtracting 4 inside the parenthesis (which is the square of half the coefficient of x), we get y = -(x^2 + 4x + 4 - 4) + 6, which simplifies to y = -(x + 2)^2 + 10. Thus, the vertex or turning point is at (-2, 10).
This shows the turning point of the parabola is at the point (-2, 10), which is a maximum since the parabola opens downwards as reflected by the negative coefficient of the x^2 term. This can be visualized on the graph of the function as the highest point on the curve. Remember that a quadratic equation represents a parabola in a Cartesian coordinate system.
Two automobiles start together from the same place and travel along the same route. The first averages 40 miles
per hour and the second 55 miles per hour. How many miles further along the route is the second car at the end of
5 hours?
Make a Selection:
A. (55 x 5) - (40 x 5)
B. 55 x 5
C. 55 - 40
D. 55/5 - 40/5
NEXT >>
Answer:
A. (55 x 5) - (40 x 5)
Step-by-step explanation:
You are solving how much miles (further along) would the second car be after 5 hours.
The first car averages 40 miles per hour. 5 hours later, it will have averaged about 200 miles in 5 hours (40 x 5 = 200).
The second car averages 55 miles per hour. 5 hours later, it will have averaged about 275 miles in 5 hours (55 x 5 = 275)
Subtract: 275 - 200 = 75
The second car would have averaged 75 more miles than the first car.
~
Answer:
A. (55 x 5) - (40 x 5)
Step-by-step explanation:
The "speedier" car goes 55 mph * 5 hrs = 55*5 miles
The "slower" car goes 40mph * 5 hrs = 40*5 miles
The distance between them is
55 *5 - 40*5
matt and brian were solving a system of equations. they both noticed that the two lines had the same slope. brian said that because each line in the system had the same slope, the two lines had to be parallel, which meant the solution to the system was "no solution" matt disagreed, and said they should also look at the y-intercepts before determining how many solutions there were. who is correct?
Answer:
Matt is correct
Step-by-step explanation:
we know that
If two lines are parallel, then their slopes are the same
In this problem we can have two cases
case 1) The two equations are equal, in this case the system has infinite solutions
case 2) The two equations have the same slope but different y-intercept, in that case the system has no solution.
therefore
Matt is correct
Matt is correct. Whether lines with the same slope are parallel or the same line depends on the y-intercepts. If y-intercepts are the same, lines are identical and have infinitely many solutions. If y-intercepts differ, lines are parallel and there's no solution.
Explanation:Matt is correct in this scenario. While it is true that lines with the same slope are either parallel or the same line, determining whether they are the same line or parallel lines requires examining the y-intercepts. If the y-intercepts are the same, then the lines are identical, and there are infinitely many solutions to the system of equations. However, if the y-intercepts are different, the lines are parallel and there is no solution to the system. So, slope, parallel lines, and y-intercept are crucial concepts in solving this problem.
Learn more about System of Equations here:https://brainly.com/question/21620502
#SPJ3