Which equation can be used to fund the nth term of the sequence an

\(x^2-8x+10=x^2-8x+16-6=(x-4)^2-6\)

Answer:

y is 0,3

Step-by-step explanation:

To find the x-intercept, substitute in

0

for

y

and solve for

x

. To find the y-intercept, substitute in

0

for

x

Answer:

(0,3)

Step-by-step explanation:

Two methods:

Method 1:  General method for any equation

Method 2: Method specific for parabolas in standard form

Method 1:  General method for any equation

For any two-variable equation to be graphed, the y-intercept is the point where the graph crosses the y-axis.  The y-axis is a vertical line through the origin (0,0).

Any y-intercept is on that line, and to get to that point starting from the origin, one can't travel left or right to get to the y-intercept point (without moving back to the y-axis).  The only movement would be up or down.

Since no left-right movement will happen, the x-coordinate is zero.

For any two-variable equation, the x and y coordinates of any point on the graph are linked by the equation.  If it is known that the x-value is zero, the y-value associated with that x-value is given by substituting zero into the equation everywhere there is an "x", and solving for "y".

\(y=-4x^2-x+3\)

\(y=-4(0)^2-(0)+3\)

Order of operations requires exponents before multiplication, or addition & subtraction...

\(y=-4(0)-(0)+3\)

multiplication...

\(y=0-0+3\)

addition & subtraction, from left to right...

\(y=3\)

So, when the x-value is zero, the y-value is three.  Therefore, the ordered pair representing that point is (0,3).

Method 2: Method specific for parabolas in standard form

The given equation is the equation for a parabola (as stated in the question), and it is given in "standard form": \(y=ax^2+bx+c\), where a, b, and c are real numbers (and a isn't equal to zero, because then the x-squared term would be zero, and the equation would really just be a linear equation).

Note that for our equation, it is in standard form if we rewrite the equation to only use addition, \(y=-4x^2+-1x+3\), where \(a=-4, ~b=-1 ~ \text{and}~c=3\)

For a parabola in standard form, the y-intercept is always at a height of "c".

So, the y-intercept would be (0,3).

Answer:

46.5482 degrees

Step-by-step explanation:

tan inverse of (5.7/5.4)

Answer:

The solution is (18,21)

Step-by-step explanation:

The picture shows the steps.

Hope this helps!!!

Step-by-step explanation:

If the scale factor of two similar solids is a: b:. then

(1) the ratio of corresponding perimeters is a:b

(2) the ratio of the base areas, of the lateral areas, and of the total areas is \(a^2: b^2\)

(3) the ratio of the volumes is \(a^3:b^3\)

Answer:

radius

Step-by-step explanation:

Answer:

I may be wrong but I think it's 14

Answer:

y= 11x

Step-by-step explanation:

find the slope: 22-11/2-1= 11/1 or 11

To find the y-intercept you can use the slope by subtracting 11 (inverse operation) from the y value of (1,11). So the y- intercept is (0,0). To write the equation plug in 11 for m and 0 for b. Since 0 has no value the equation would be y= 11x

Answer:

x=\(-\frac{14}{3}\)

Step-by-step explanation:

3x-12-6x+21=23

-3x+9=23

-3x=14

x=\(-\frac{14}{3}\)

Answer:

57327392393629324

Step-by-step explanation:

Answer:

What the answer

Step-by-step explanation:

Pls

Answer:

Reflect it across the Y axis then do a 90 degree CCW rotation.

Step-by-step explanation:

Answer:

\(f(x) = \frac{1}{2}x + 5\)

Step-by-step explanation:

So you can generally express a linear function use the slope-intercept form as such: \(y=mx+b\) where m=slope, and b=y-intercept.

The y-intercept is defined as the value of f(0), since when the line crosses the y-axis, the x-value is 0, and as provided in the table that value is 5, so we have the function rule: \(f(x) = mx+5\)

The slope is defined as how much y-changes, as x increases by 1. We can generally use the formula: \(m=\frac{y_2-y_1}{x_2-x_1}\) and this can be found using any two points, since the slope is constant.

We can use the two points (0, 5) and (2, 6) and plug it into the equation, to find the rise/run

\(\frac{6-5}{2-0} = \frac{1}{2}\)

So plugging this into the slope-intercept form you get the function

\(f(x) = \frac{1}{2}x + 5\)

Answer:

\(x = \frac{33}{5} \)

or

\(x = 6 \frac{3}{5} \)

or

\(x = 6.6\)

Step by Step:

Step 1: Rewrite the equation (I used x instead of k.)

\( \frac{x}{4} = \frac{33}{20} \)

Step 2: Make x a loner by moving the 4 to the right side.

\(4 \times \frac{x}{4} = \frac{33}{20} \times 4 \)

Step 3: Cancel multiplied terms on the left, multiply numbers on the right.

\(x = \frac{165}{100} \)

Step 4: Simplify.

\( x = \frac{33}{5} \)

The distance from the pole at which the cable is anchored is about 25 feet from the pole .

Given that a 35-foot cable is run from the top of the pole and anchored to the ground at a distance from the pole. The problem is to determine about how far away from the pole would it be anchored.

Let AB be the pole of length 40 feet, and CD be the 35-foot long cable anchored to the ground at D and attached to the top of the pole at C. Let E be the point on the ground at which the cable is taut and is anchored. The distance ED is to be determined.

we can see that ∆CDE is a right-angled triangle with ∠CED = 90°.

Using Pythagoras Theorem, we have:CD² = CE² + DE²35² = (40 - ED)² + DE² .

Simplifying the above equation

1225 = 1600 - 80ED + ED²

1225 - 1600 + 80ED - ED² = 0ED² - 80ED + 375 = 0

Factorizing the above quadratic equation

ED² - 25ED - 15ED + 375 = 0ED(ED - 25) - 15(ED - 25)

  = 0(ED - 15)(ED - 25) = 0So, ED = 15 ft or ED = 25 ft.

The negative value of ED is extraneous since it represents a point below the ground, which is not possible. Therefore, the distance from the pole at which the cable is anchored is about 25 feet from the pole.

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Answer:

Answer is 2

Step-by-step explanation:

To get rid of the fraction:

5*4x-5 =3

5

4x-5=3

4x=3+5

4x=8

x=2

Step-by-step explanation:

It should be 5x4= 20

-5=15

15÷5

=3

The simplified form of \(a^2 + 2ab + b^2 / -2a\) is \(- (a+b)^2 / 2a.\)

What is an algebraic expression?

An algebraic expression is a mathematical phrase that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. Algebraic expressions are used to represent quantities or values that can vary, depending on the values assigned to the variables in the expression. Algebraic expressions can be simple or complex, and they can have one or more variables.

To simplify the expression \(a^2 + 2ab + b^2 / -2a\), we can follow the steps below:

1) Factor the numerator \(a^2 + 2ab + b^2\) using the formula \((a+b)^2 = a^2 + 2ab + b^2\). This gives us:

\((a+b)^2 / -2a\)

2) Simplify the expression (a+b)^2 by expanding it:

\(a^2 + 2ab + b^2 / -2a\)

3) Replace the numerator in the expression with the expanded form of \((a+b)^2\):

\((a^2 + 2ab + b^2) / -2a\)

4) Distribute the negative sign across the terms in the numerator:

\((-a^2 - 2ab - b^2) / 2a\)

5) Factor out a negative sign from the numerator:

\(-(a^2 + 2ab + b^2) / 2a\)

6) Simplify the expression in the numerator by recognizing that it is the negative of (a+b)^2:

\(- (a+b)^2 / 2a\)

Therefore, the simplified form of \(a^2 + 2ab + b^2 / -2a\) is \(- (a+b)^2 / 2a.\)

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The dimensions of the rectangle are 4 ft by 5 ft.

Given that the length of a rectangle is 3 ft less than twice the width, and the area of the rectangle is 44 sq.ft. We have to find the dimensions of the rectangle. Let's consider the width of the rectangle as x ft.Length of the rectangle = (2x - 3) ftArea of the rectangle = Length x Width44 = (2x - 3) x x44 = 2x^2 - 3x44 = x (2x - 3)2x^2 - 3x - 44 = 0To solve for x, we will factorize the equation by splitting the middle term.2x^2 - 8x + 5x - 20 = 0Factorize2x(x - 4) + 5(x - 4) = 0(x - 4) (2x + 5) = 0x = 4 ft (since the width of a rectangle can't be negative)or 2x = -5This gives us an invalid value, so x = 4 ftNow that we have the width of the rectangle, we can calculate the length as follows:Length of the rectangle = (2x - 3) ftLength of the rectangle = (2 * 4) - 3Length of the rectangle = 8 - 3Length of the rectangle = 5 ft.

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Answer:

C. -1 over 2

Step-by-step explanation:

Points: (-2,2) and (0.1)

slope is m=(y2-y1)/(x2-x1)= (1-2)/(0+2)= -1/2

Option C

Using a confidence interval of 90%, note that the Margin of Error is computed to be: 4.171

The margin of error is a statistic that expresses the degree of random sampling error in survey data. The greater the margin of error, the less confident one should be that a poll result would accurately represent the results of a population census.

The margin of error for a 90% confidence interval for the population mean can be calculated using the following formula:

Margin of Error = z* (σ/√n)

where:

z* is the z-score corresponding to the level of confidence,

σ is the population standard deviation, and n is the sample size.

For a 90% confidence level, the corresponding z-score can be found using a standard normal distribution table or calculator.

The z-score for a 90% confidence level is 1.645.

Plugging in the values, we get:

Margin of Error = 1.645 * (19/√43)

Margin of Error ≈ 4.171

Rounded to three decimal places, the margin of error is approximately 4.171.

Therefore, we can say with 90% confidence that the true population mean lies within the range of the sample mean plus or minus 4.171.

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The given differential equation is a third-order linear homogeneous equation.

According to the Existence and Uniqueness Theorem, a unique solution exists if the coefficients of the differential equation are continuous on the given interval, which is the case here. Since the initial conditions y″(0) = 2, y'(0) = 1, and y(0) = 0 are also given, the existence and uniqueness of a solution are guaranteed by the theorem. Therefore, the given differential equation is guaranteed to have a unique solution on the specified interval. A differential equation is an equation that relates a function to its derivatives (or differentials) of one or more independent variables. In other words, it expresses a relationship between an unknown function and its rate of change.

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The complete question is :

According to the Existence and Uniqueness Theorem, which of the following differential equations are guaranteed to have a unique solution on the specified interval. Explain your reasoning.

x2d3ydx3-4x-1d2ydx2+3dydx+2y=0,y″(0)=2,y'(0)=1,y(0)=0

"What is the area of the floor in this classroom?" is not a statistical question.

Statistical Reasoning is the first course in statistics for students whose college and career paths require knowledge of the fundamentals of the collection, analysis, and interpretation of data.

All statistical questions contain gathering numerical statistics (normally from a set of human beings) after which studying it to attract conclusions approximately the reviews of human beings of a positive phenomenon because the statistics vary relying on the reaction of every person.

This method isn't required to decide the location of the ground due to the fact this has a completely unique solution and might certainly be located via way of means of measuring the peak and width of the school room after which multiplying each number.

therefore, this doesn't mean accumulating loads of statistics and the statistics does now no longer vary.

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The dimensions of the rectangular box are given as follows:

All the dimensions.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The box's volume is obtained as follows:

54 x 1³ = 128 x (3/4)³ = 54 cubic inches. (the volume of a cube is the side length cubed)

Hence all the options can be the dimensions of the box, as all the options have a multiplication resulting in 54.

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The linear relationship illustrated in the provided table can be effectively described by the equation Y = -4x + 2. Option D.

To determine the equation that represents the given table with the values of x and y, we can observe the pattern and find the equation of the line that fits these points.

Given the table:

X: 2 0 4

Y: -4 3 1

We can plot these points on a graph and see that they form a straight line.

Plotting the points (2, -4), (0, 3), and (4, 1), we can see that they lie on a line that has a negative slope.

Based on the given options, we can now evaluate each equation to see which one represents the line:

Y = 1/2x + 5

When we substitute the x-values from the table into this equation, we get the following corresponding y-values: -3, 5, and 6. These values do not match the given table, so this equation does not represent the table.

Y = -1/2x + 3

When we substitute the x-values from the table into this equation, we get the corresponding y-values: 4, 3, and 2. These values also do not match the given table, so this equation does not represent the table.

Y = 2x - 3

When we substitute the x-values from the table into this equation, we get the corresponding y-values: -4, -3, and 5. These values do not match the given table, so this equation does not represent the table.

Y = -4x + 2

When we substitute the x-values from the table into this equation, we get the corresponding y-values: -6, 2, and -14. Interestingly, these values match the y-values in the given table. Therefore, the equation Y = -4x + 2 represents the table.

In conclusion, the equation Y = -4x + 2 represents the linear relationship described by the given table. So Option D is correct.

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Mia's age 7.01424×10⁶ in years , months and days is 13 years 4 months 6 days .

In the question ,

it is given that ,

Mia is 7.01424×10⁶ minutes old ,

it is known that  1 day = 24 hours

and 1 hour = 60 min

So 1 day = 24*60 = 1440min

Hence 1440 min = 1 day

we get 1 min = 1/1440 day

multiplying both sides by 7.01424×10⁶

7.01424×10⁶ min = (7.01424×10⁶)/1440 days

= 4871 days

Now we need to convert 4871 days into years and months

it is given that  365 days = 1 year

so 1 day = 1/365 year

multiplying both sides by 4871

we get

4871 days = 4871/365 year

= 13 years + 126 days   ...(i)

we know that 30 days = 1 month

so 120 days = 4 months

hence 126 days = 4 months + 6 days   ....(ii)

Substituting the value from equation(ii) in equation(i) .., we get

4871 days  = 13 years + 4 months + 6 days .

Therefore ,On Converting Mia's age 7.01424×10⁶ in years ,months and days is 13 years 4 months 6 days .

The given question is incomplete , the complete question is

Mia is 7.01424×10⁶ minutes old. Convert her age to more appropriate units using years, months, and days . Assume a year has 365 days and a month has 30 days.

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The equivalent expression for five eighths raised to the negative first power times forty-two hundredths raised to the second power is option B

(5/8)^-1 × (0.42)^2

= {1 ÷ (5/8)¹} × 0.42²

= {1 × (8/5)¹} × 0.42²

= (8/5)¹ × 0.42²

Therefore, the equivalent expression is eight fifths raised to the first power times the quantity one over forty-two hundredths raised to the second power

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Answer:

(1.6) (0.42)^2 C

Step-by-step explanation:

I had originally put B, but my teacher explained and said its C.

the first part of b is correct where it says 8/5, bc you need to flip it in order to not have a negative exponent (you cant have a negative exponent as an answer) but 0.42 is correct and iit does not need to be fliped, since there is no (8/5)(0.42)^2 option, you need to make the 8/5 into a decimal, it becomes 1.6 and so the answer is C