The value of y varies directly with x. If x=8 then y=80. What is the value of x when y = 120?

Answer:

2 = 74

1 = 106

Step-by-step explanation:

none

To solve for x in the equation 4x3 = -5x - 21, we can follow these steps:

1. Move all the terms containing x to one side of the equation, and move the constant term to the other side. We can do this by adding 5x to both sides and then adding 21 to both sides:

   4x3 + 5x = -21

2. Factor out x from the left-hand side of the equation:

   x(4x2 + 5) = -21

3. Divide both sides by (4x2 + 5):

   x = -21 / (4x2 + 5)

So the solution for x is x = -21 / (4x2 + 5). Note that this is a rational function, which means that the value of x depends on the value of the variable x. This equation has no real solutions because the denominator is always positive, and the numerator is negative.

The expression (-3)0 has a value of 0 when evaluated because a number multiplied by 0 gives 0

From the question, we have the following parameters that can be used in our computation:

(-3)0

The above statement is a product expression that multiplies the values of -3 and 0

Also, there is no need to check if there are like terms in the expression or not

This is  because we are multiplying the factors

So, we have

(-3)0 = 0

This means that the value of the expression is 0 i.e a number multiplied by 0 gives 0

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The recursive sequence that represents the sequence defined by the following explicit formula is given as follows:

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

The explicit formula of the sequence is given as follows:

\(a_n = a_1q^{n-1}\)

In which \(a_1\) is the first term.

The first term and the common ratio for this problem is given as follows:

\(a_1 = -32, q = -\frac{1}{4}\)

The common ratio means that each term is the previous term multiplied by -1/4, hence the recursive formula is given as follows:

\(a_{n + 1} = -\frac{1}{4}a_n\)

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Answer:

NSL

Step-by-step explanation:

The angle number which represents an angle adjacent to ∠PSL is interior ∠1.

A transversal is a line that intersects two lines at two different points.

When a transversal intersects two lines at two different points two pairs of interior and exterior angles are formed.

If a transversal intersects two lines that are parallel to each other then the pair of corresponding and alternate angles are of the same measure.

We know adjacent angles share a common side.

In the given diagram ∠PSL is adjacent to ∠KRL because these two angles share a common side which is Line LM.

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The expression (X - Y) 5 ÷ 8 - 1 ÷ 4 (X + Y) is equivalent to

(20X² - 20Y² - 1) / (4X + 4Y)

We have,

We can simplify the given expression as follows:

(X - Y) 5 ÷ 8 - 1 ÷ 4 (X + Y)

= (5X - 5Y) ÷ 8 - 1 ÷ (4X + 4Y)

[distributing the factors]

= (5X - 5Y) /8 - 1/(4X + 4Y)

[finding a common denominator]

= ((5X - 5Y)(4X + 4Y) - 1)/(4X + 4Y)

= (20X² + 20XY - 20XY - 20Y² - 1) / (4X + 4Y)

= (20X² - 20Y² - 1) / (4X + 4Y)

Therefore,

The expression (X - Y) 5 ÷ 8 - 1 ÷ 4 (X + Y) is equivalent to

(20X² - 20Y² - 1) / (4X + 4Y)

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Answer:

The equation a + d(n-1)

Step-by-step explanation:

Where a is the first number in the sequence, d is the common difference and n is the position of a certain number in the series, e.g

1, 2, 3, 4, 5: a = 1, d = 1 (because 2-1=1, 3-2=1, 4-3=1, etc) and n = 1,2,3...

2, 4, 6, 8, 10: a = 2, d = 2 (because 4-2=2, 6-4=2, etc) and n = 1,2,3,4,5...

So for the second sequence, we could try to get the value of n in n = 6 as follows:

a + d(n-1) where a = 2, n = 6 and d = 2

Thus, 2 + 2(6-1) = 2 + 2(5) = 2 + 10 = 12

So the sixth number in the series would be 12

The two figures show equivalent graphs because:

A. The graphs have several edges that match the number of vertices.

B. The graphs have the same number of edges.

C. The vertices are connected in the same way.

D. The graphs have the same number of vertices.

The third equivalent graph is at option D.

The graphs that have the same number of vertices connected in the same way are called equivalent graphs. If they are connected in the same way then their count of edges will be the same for both graphs. They are also said to be isomorphic graphs.

The given graphs have
Graph1: vertices BCJK

Graph2: vertices BCJK

So, there is the same number of vertices for both graphs.

The connection between the vertices:

Graph1: J - B - C - K - B

Graph2: J - B - C - K - B

So, they are connected in the same way.

The edges formed by these vertices:

Graph1: JB; BC; CK; KB

Graph2: JB; BC; CK; KB

So, there is the same number of edges for both graphs.

Here the number of edges = the number of vertices i.e., (4 = 4)

From all these comparisons, the given graphs are equivalent.

The third equivalent graph made from these graphs is at option D in the diagram attached below.

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Disclaimer: The given question is incomplete. There is no image attached in the given question. Here the image is attached.

An image of triangle NOG after a rotation 90° clockwise about the origin is shown below.

In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Next, we would apply a rotation of 90° clockwise about the origin to the coordinate of this triangle NOG in order to determine the coordinate of its image;

(x, y)                →            (y, -x)

Point N = (-4, -1)          →     Point N' (-1, 4)

Point O = (-4, -3)          →     Point O' (-3, 4)

Point G = (0, -1)          →     Point G' (-1, 0)

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Answer:

mean = 24

Step-by-step explanation:

the mean is calculated as

mean = \(\frac{sum}{count}\)

the sum of the data set is

sum = 12 + 13 + 15 + 28 + 28 + 30 + 42 = 168

there is a count of 7 in the data set , then

mean = \(\frac{168}{7}\) = 24

Answer:

you divide and muliply til you have got to an hour and then qadd it all

Step-by-step explanation:

Answer: To find the image of a figure under a translation, you need to apply the same translation to every point in the figure.

In this case, the image of hexagon DEFGHI is hexagon D′E′F′G′H′I′. To find the image of each point, you can apply the translation that maps point D to point D′.

For example, to find the image of point E under the translation, you can apply the same translation that maps point D to point D′:

Point D is located at (2, 5).

Point D′ is located at (-6, -2).

The translation that maps point D to point D′ is a translation 6 units to the left and 2 units down.

To find the image of point E under this translation, you can apply the same translation to point E:

Point E is located at (5, 5).

The image of point E is located at (5 - 6, 5 - 2) = (-1, 3).

You can follow the same process to find the images of the other points under the translation.

Alternatively, you can use the coordinates of point D and point D′ to find the translation vector that describes the translation. The translation vector is a displacement that describes the change in position of a point under the translation.

In this case, the translation vector is given by the displacement from point D to point D′:

Point D is located at (2, 5).

Point D′ is located at (-6, -2).

The translation vector is given by the displacement (-6 - 2, -2 - 5) = (-8, -7).

To find the image of any point under the translation, you can add the translation vector to the coordinates of the point. For example, to find the image of point E under the translation, you can add the translation vector to the coordinates of point E:

Point E is located at (5, 5).

The translation vector is (-8, -7).

The image of point E is located at (5 - 8, 5 - 7) = (-3, -2).

You can follow the same process to find the images of the other points under the translation.

Step-by-step explanation:

Answer: The sum of the two polynomials 3m^2 + 4m + 7 and 4m^2 - 3m + 2 is 7m^2 + m + 9.

Step-by-step explanation:

Answer:

4 (x) + 4 (2)

Step-by-step explanation:

A power series representation for the function the interval of convergence is x > -14 .

Given :

a power series representation for the function. (Give your power series representation centered at x = 0.) f(x) = 1273 Determine the interval of convergence.

f ( x ) = 3 / 17 + x

Interval of convergence :

The interval of convergence can be calculated once you know the radius of convergence. First you solve the inequality |x − a| < R for x and then you check each endpoint individually.

3 / 17 + x < 1

3 < 1 * ( 17 + x )

3 < 17 + x

-14 < x

x > -14

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Answer:

23/20        

Step by step Explanation

Answer:

Step-by-step explanation:

\(2-\frac{3}{4}-1\frac{1}{10}=x\\x=2-\frac{3}{4}-\frac{11}{10}\\\mathrm{Convert\:element\:to\:fraction}:\quad \:2=\frac{2}{1}\\x=\frac{2}{1}-\frac{3}{4}-\frac{11}{10}\\1,\:4,\:10\\\mathrm{Prime\:factorization\:of\:} ;\\1=1\\4=2\times \:2\\10=2\cdot \:5\\\mathrm{Multiply\:the\:numbers:}\:2\times \:2\times \:5=20\\Adjust\: fractions\: based\: on\: their\: LCM ;\\\frac{2}{1}=\frac{2\times \:20}{1\times \:20}=\frac{40}{20}\\\\\frac{3}{4}=\frac{3\times \:5}{4\times \:5}=\frac{15}{20}\\\)

\(\frac{11}{10}=\frac{11\times \:2}{10\times \:2}=\frac{22}{20}\\\mathrm{Since\:the\:denominators\:are\:equal,\\\:combine\:the\:fractions}:\\\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\\\\mathrm{Subtract\:the\:numbers:}\:40-15-22=3\\\\x=\frac{3}{20}\)

Answer:

7, 2, -3, -8

Step-by-step explanation:

y = -5x + 2  Substitute in -1 for x

y = -5(-1) + 2

y = 5 + 2

y = 7

y = -5x + 2  Substitute in 0 for x

y = -5(0) + 2

y = 0 + 2

y = 2

y = -5 + 2 substitutes in 1 for x

y = -5(1) + 2

y = -5 + 2

y = -3

y = -5x + 2  Substitute in 2 for x

y = -5(2) + 2

y = -10 + 2

y = -8

Helping in the name of Jesus.

Answer:

13.9

Step-by-step explanation:

Answer:

To find the radius from the circumference of a circle, you have to do the following:

Divide the circumference by π, or 3.14 for an estimation. The result is the circle's diameter.

Divide the diameter by 2.

There you go, you found the circle's radius.

hace 6 días

Answer:

To calculate how much you would have to deposit today to accumulate the same amount of money that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn, we can use the formula for the present value of an annuity due:

PV = PMT × ((1 - (1 + r/n)^(-n×t)) / (r/n)) × (1 + r/n)

where:

- PV is the present value of the annuity due (the amount you would have to deposit today)

- PMT is the monthly payment ($75)

- r is the annual interest rate (3.5%)

- n is the number of times interest is compounded per year (12 for monthly compounding)

- t is the number of years (10)

PV = 75 × ((1 - (1 + 0.035/12)^(-12×10)) / (0.035/12)) × (1 + 0.035/12) = **$7,360.47**

Therefore, you would have to deposit **$7,360.47** today to accumulate the same amount of money that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn.

Answer:

Step-by-step explanation:

Given Equation :

\(y = \frac{1}{2} x - 3\)

Which is in slope intercept form :

\(y = mx + b\)

Where :

m = slope

b = y-intercept.

Thus , in the given Equation , the y-intercept is -3

Step-by-step explanation:

the diagaonls of rectangle interscet at x

find the angle that a diagaonl makes a longer side of the rectangle

anywhere you see x, input the value in the brackets.

eg f(-2) = 2(-2)+8

= -4+8

=4

Answer:

if x= -2

then f(x) = 2×(-2)+8

= -4+8

= 4

if x=0

then f(x)=2×0+8

=0+8

=8

if x=5

then f(x)=2×5+8

=10+8

=18

The Area of Square is 81 cm².

let the side of the square which is length for both rectangles be a.

let the width of rectangle be x and y.

So, x+ y= a

sum of perimeters= 54

2 (a +x ) + 2 (a+ y) = 54

2a+ 2x + 2a+ 2y = 54

2a + 2a + 2(x+ y) = 54

4a + 2 (a) = 54

4a + 2a = 54

6a = 54

a= 54/6

a= 9

So, area of square

= 9 x 9

= 81 cm²

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Answer:

answer: negative five eighths

The solution to the expression one half cubed − 6 ÷ square root of 64 is A. negative five-eighths.

Given a fractional expression:

One half cubed − 6 ÷ square root of 64

It is required to find the value of the expression.

This can be numerically written as:

\((\frac{1}{2} )^3-6\div\sqrt{64}\)

It is known that:

\(\sqrt{64}=8\)

So, the expression can be written as:

\((\frac{1}{2} )^3-6\div8\)

Now, \((\frac{1}{2} )^3=\frac{1}{2^3}\)

                \(=\frac{1}{8}\)

So, the expression becomes:

\((\frac{1}{8} )-6\div8\)

Using the BODMAS rule, division has to be done first before subtraction.

So, the expression becomes:

\((\frac{1}{8} )-\frac{6}{8}=-\frac{5}{8}\)

Hence, the correct option is A. negative five-eighths.

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The circle graph shows that most respondents (68%) hide their mess in the closet, while a significant minority (23%) shove things under the bed. Only a small percentage of respondents put things in the bathtub (6%) or the freezer (3%), with the freezer being the least popular option.

To create a circle graph for this survey data, we need to calculate the percentage of respondents for each category and then represent it as a fraction of the total 360 degrees of the circle.

Percentage of respondents who toss their mess in the closet: 68%

Percentage of respondents who shove things under the bed: 23%

Percentage of respondents who put things in the bathtub: 6%

Percentage of respondents who put the mess in the freezer: 3%

To convert these percentages into fractions of the total 360 degrees, we can multiply each percentage by 360/100:

Fraction of circle for closet: 68% x 360/100 = 244.8 degrees

Fraction of circle for under the bed: 23% x 360/100 = 82.8 degrees

Fraction of circle for bathtub: 6% x 360/100 = 21.6 degrees

Fraction of circle for freezer: 3% x 360/100 = 10.8 degrees

We can then draw a circle with 360 degrees and divide it into four sections based on these fractions. We can label each section with the corresponding category and the fraction/percentage it represents.

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Answer: The 2 answers are inequality form and interval notation: n>200, and (200, ∞).

Step-by-step explanation: To solve for n, you’ll need to simplify the both sides of the inequality, and then isolating the variable.

Answer:

Step-by-step explanation:

The population of bacteria in the culture after 7 hours is approximately 883.

Several real-world phenomena, including population expansion, radioactive decay, compound interest, and the spread of diseases, are modeled using exponential functions. In calculus, where they are used to define the exponential and logarithmic functions—essential ideas in calculus and other fields of mathematics—they also play a significant role.

Using the formula \(P_t = P_0 \times 2^{\frac{t}{d}}\), where P_t is the population after t hours, P₀ is the initial population, t is the time in hours and d is the doubling time, we can find the population of bacteria in the culture after 7 hours as follows:

Since the initial population is 470, we have P₀ = 470.

The doubling time is 8 hours, so we have d = 8.

Substituting these values into the formula, we get:

\(P_7 = 470 \times 2^{\frac{7}{8}}\)

P₇≈ 882.77

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Answer:

n = 24

Step-by-step explanation:

60= n/3 + 52

-52. -52

8= n/3

You then take 3/1 times 8 therefore you leave n by itself

n = 24