algebra 1
what is the written formula for standard form

The value of a in the function f(x) = ax² + 7x + 2 when differentiated is 13/x

Given that the function is represented as

f(x) = ax² + 7x + 2

Also, we have the differentiated function to be

∆ = 33​

This means that we differentiate f(x) and set the value to 33

When f(x) is differentiated, we have

∆ = 2ax + 7

By equating the functions, we have

2ax + 7 = 33

This gives

2ax = 26

So, we have

a = 13/x

Hence, the value of a is 13/x

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Answer:600

Step-by-step explanation:

Since this number is less than 5, we round down the number, i.e. we round it off to the nearest 100 that comes next to this number. So, 15 becomes 00 which on adding to 6 at the hundred's places, becomes 600.

Answer:

  1/2

Step-by-step explanation:

You want the limit ...

  [tex]\displaystyle \lim_{t\to\infty}{\dfrac{t-3}{\sqrt{4t^2+25}}}[/tex]

In general, for polynomial-like functions, the limit is the ratio of the highest-degree terms:

  [tex]\displaystyle \lim_{t\to\infty}{\dfrac{t-3}{\sqrt{4t^2+25}}} = \lim_{t\to\infty}{\dfrac{t}{\sqrt{4t^2}}}=\dfrac{t}{2t}=\boxed{\dfrac{1}{2}}[/tex]

You can consider the limit when x→0 and t=1/x.

  [tex]\displaystyle \lim_{t\to\infty}{\dfrac{t-3}{\sqrt{4t^2+25}}} = \lim_{x\to 0}{\dfrac{\dfrac{1}{x}-3}{\sqrt{\dfrac{4}{x^2}+25}}}\\\\\\=\lim_{x\to 0}\dfrac{1-3x}{\sqrt{4+25x^2}}=\dfrac{1}{\sqrt{4}}=\boxed{\dfrac{1}{2}}[/tex]

Answer:

i don't know

Step-by-step explanation:

you didn't put that answers

Answer:

I believe it's B!

Step-by-step explanation:

To get System B from System A, we can use the operation of replacing one equation with a multiple of the other equation. Specifically, we can multiply the first equation of System A by 4 to get:

{32x - 12y = 0, 2x + 7y = 3}

Now, we can see that the first equation of System B is the same as the first equation of the modified System A. The second equation of System B is also equivalent to the second equation of the modified System A, since we can multiply the second equation of the modified System A by 4/2 to get:

{32x - 12y = 0, 8x + 28y = 12}

Therefore, System B can be obtained from System A by replacing one equation with a multiple of the other equation. The correct answer is B.

Hope this helps, I'm sorry if it doesn't! If you need more help, ask me!

the answer is 5x^2+5x+4

Answer:

5x^2+5x+4

Step-by-step explanation:

also can someone help me with my questions

The length of segment BD, considering the Geometric Mean Theorem, is given as follows:

C. 8 units.

The geometric mean theorem in a triangle states that the length of a line segment joining the midpoints of two sides of a triangle is equal to the geometric mean of the lengths of those two sides.

The lengths of the two sides for this problem are given as follows:

4 and 16.

Hence the length of segment BD is obtained with the geometric mean of 4 and 16, as follows:

BD = sqrt(4 x 16)

BD = sqrt(64)

BD = 8 units.

Hence the correct option for this problem is given by option C.

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The line of best fit for this set of points is y = -1.00x + 9.00.

Coefficient is a value that is used to indicate the degree or amount of a certain property or characteristic. It is usually used in mathematics and physics, and is a numerical measure of how two variables are related. For example, the coefficient of friction is a number that indicates how much resistance there is between two surfaces when one is sliding over the other. In economics, the coefficient of elasticity is used to measure how much of a change in one variable affects a change in another.

Linear regression is a technique used to find the line of best fit for a given set of points. To use linear regression, we must first calculate the mean of all the x and y coordinates. The mean of the x coordinates is 4, and the mean of the y coordinates is 4.5.

We then calculate the sum of the squared differences between the x and y coordinates and their respective means. This sum is 36.5.

Next, we calculate the sum of the products of the differences between the x and y coordinates and their respective means. This sum is -25.

Using the formula for linear regression, we can calculate the slope of the line of best fit. The slope is -1.00.

To calculate the y-intercept of the line of best fit, we use the slope and the mean of the x and y coordinates. The y-intercept is 9.00.

The line of best fit for this set of points is y = -1.00x + 9.00.

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The final point after both reflections would be (8, 5).

what is a graph?

A graph is a visual representation of data, typically in the form of a diagram or chart, used to show the relationship between different variables or quantities. Graphs are commonly used to display data in a way that makes it easier to understand and analyze.

Graphs can take many different forms, depending on the type of data being presented and the purpose of the graph. Some common types of graphs include:

Line graphs: Used to show trends over time.

Bar graphs: Used to compare different values or quantities.

Pie charts: Used to show the proportion of different components of a whole.

Scatter plots: Used to show the relationship between two variables.

Histograms: Used to show the frequency distribution of a set of data.

To reflect a point across the x-axis, we simply change the sign of the y-coordinate. So if we start with the point (-8, -5), its reflection across the x-axis would be (−8, 5).

To reflect a point across the y-axis, we change the sign of the x-coordinate. So reflecting the point (−8, 5) across the y-axis would give us (8, 5).

Therefore, the final point after both reflections would be (8, 5).

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The student applied the reflection before the translation, which is incorrect. (error) The correct sequence of transformations is a translation followed by a reflection across the vertical line. (Correct response)

In mathematics, a sequence is an ordered list of numbers, usually denoted by {a1, a2, a3, ...}, where each element in the list is called a term or a member of the sequence. Sequences can be finite or infinite, and they can be defined by a formula, a recursive rule, or simply by listing the terms.

by the question.

The student's mistake is that a reflection followed by a translation is not equivalent to just a translation. In other words, the order of the transformations matters.

To correct the mistake, the student could perform the translation first and then the reflection across the vertical line.

The student did not specify the location of the vertical line of reflection. The correct response is to specify the line of reflection that maps the corresponding sides of the trapezoids onto each other.

To correct the mistake, the student would need to carefully analyze the two trapezoids and their corresponding parts, and consider whether any stretching or skewing is necessary to achieve an exact mapping. Alternatively, the student could use a different method of transformation, such as a rotation or a combination of rotations and translations.

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Therefore , the solution of the given problem of equation comes out to be x = -14/15 and y =  -37/15 .

It is standard practise in mathematical formulas to employ a single variable term to ensure agreement between competing claims. Equations, which are mathematical statements, are used to demonstrate the equality of many academic integers numbers. Instead of dividing 12 into 2 parts in this instance, the normalise technique adds b + 6 to use the data from y + 6.

Here,

We can use the substitution or elimination technique to solve this system. Here, we'll employ the removal strategy.

given solution system:

=> y = 3x + 1 (1)

=>-x + 2y = -3 (2) (2)

By combining equations (1) and (2) multiplied by 1 and 3, respectively, we can remove the variable x:

=>3*(-x + 2y = -3)

=> -3x + 6y = -9

=> 1*(y = 3x + 1)

=> y =  3x + 1

Combining the two equations:

=>y = 3x + 1

=> -3x + 6y = -9

=> 6y - 3x = -8

By multiplying both parts of this equation by 3, we can make it simpler:

=> 2y - x = -8/3

However, we can still use equation (1) to replace y even though we have a new equation in terms of x and y:

=> y = 3x + 1

=> 2y - x = -8/3

y = 3x Plus 1 is substituted in the second equation:

=>2(3x + 1) - x = -8/3

=> 6x + 2 - x = -8/3

=>5x = -14/3

=>x = -14/15

Finding y by substituting this x number in equation (1):

=> y = 3x + 1 = 3(-14/15) + 1 = -37/15

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The height of the tubes is 11.68 inch  

The formula for the surface area of a cylinder is:

Where

Here we have

The surface area of the tube is 172 in² and the radius is 2 inches.  

Using the formula,

Surface area of Tube  = 2π (2) (2+ h)

= 4π(2 + h)

From the given data,

The surface area of the tube = 172  

=> 4π(2 + h) = 172

=> π(2 + h) = 43    

=> 44/7 + 22h/7 = 43

=> 44 + 22h = 301

=> 22h = 257

=> h = 11.68 inch  

Therefore,

The height of the tubes is 11.68 inch  

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If  the perimeter of a square field is 64 m. If the field is surrounded by a running path of width 3.5 m. The area of the path surrounding the square field is 273 square meters.

Let's denote the side length of the square field as x meters.

The perimeter of a square is given by the formula: Perimeter = 4 * side length

Write the equation:

4x = 64

Divide both sides by 4:

x = 16

So, the side length of the square field is 16 meters.

Now, we need to find the area of the path surrounding the field.

The new side length of the square including the path is: x + 2 * (width of the path)

Substitute

New side length = 16 + 2 * 3.5 = 23 meters

The area of the path:

Area of path = Area of larger square - Area of original square

Area of larger square = (New side length)^2

= 23²

= 529 square meters

Area of original square = (Side length)²

= 16²

= 256 square meters

Area of path = 529 - 256

= 273 square meters

Therefore  the area of the path surrounding the square field is 273 square meters.

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Considering the square field of each side 16 m, once the 3.5 m wide path is added around the square, the total area increases. The difference between the area of the larger square and the original square gives the area of the path as 273 sq m.

This problem can be solved focusing on square geometry and area calculations. We begin by understanding that the perimeter of the square is 64 m. Since a square has equal sides, each side measures 16 m (i.e., 64 m divided by 4).

The running path that surrounds the field adds a width of 3.5 m around the square. So the total side length of the larger square (field + path) becomes 16 m + 3.5 m + 3.5 m = 23 m.

The total area of the larger square (field + path) is thus 23 m * 23 m = 529 sq m.

Now we subtract the area of the original field (16 m * 16 m = 256 sq m) from this total. Therefore, the area of the path is 529 sq m - 256 sq m = 273 sq m.

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Answer:

Option D

Step-by-step explanation:

Total number of posters Rhett puts up = 9

                Printing cost of each poster = $2

                                    ∴Total cost on posters = ([tex]\frac{2 dollars}{1 poster}[/tex]) × (9 posters)

                                                                           = $18

Note: The unit multiplier used above is arranged in a way that the current unit of “posters” is cancelled out and the answer is assigned with the new unit of “dollars".

Number of fliers Rhett gives out = x

Printing cost of each flier = $0.20

                                    ∴Total cost on fliers = [tex]\frac{0.20 dollars}{1flier}[/tex] × (x fliers)

                                                                      = $0.20x

Note: The unit multiplier used above is arranged in a way that the current unit of “fliers” is cancelled out and the answer is assigned with the new unit of “dollars”

∴How much it cost Rhett to search for his lost puppy:

y = Total cost on fliers + Total cost on posters

∴[tex]y = 0.20x + 18[/tex]

∴Option D

The prοbability οf getting vοwel card twice is 6.25%

Prοbability is a way οf calculating hοw likely sοmething is tο happen. It is difficult tο prοvide a cοmplete predictiοn fοr many events. Using it, we can οnly fοrecast the prοbability οr likelihοοd, οf an event οccurring. The prοbability might be between 0 and 1, where 0 denοtes an impοssibility and 1 denοtes a certainty.

Here Tοtal number οf card frοm A tο L = 12.

The vοwel between A tο L = A,E,I

Number οf vοwel = 3

Nοw the prοbability

=> Number οf favοrable incοme/ Tοtal number οf οutcοme

Here Tο draw vοwel  in first, the prοbability =  3/12= 1/4

Nοw again the prοbability οf drawing vοwel in secοnd = 3/12 = 1/4.

Then probability of getting vowel twice = [tex]\frac{1}{4} \times \frac{1}{4}[/tex] = 1/16

=> [tex]\frac{1}{16}\times100[/tex] = 6.25%.

Hence the probability of getting vowel card twice is 6.25%.

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The radian measure of the angle that forms an arc of length 38 inches in Circle O is approximately 1.9 radians.

What is an angle ?

The length of an arc of a circle is given by the formula:

length of arc = radius * angle in radians

Let x be the radian measure of the angle that forms an arc of length 38 inches in Circle O. Then we can write:

38 = 20x

Solving for x, we get:

x = 38/20

x = 1.9 radians (to the nearest tenth)

Therefore, the radian measure of the angle that forms an arc of length 38 inches in Circle O is approximately 1.9 radians.

What is an arc?

In geometry, an arc is a segment of a curve, such as a circle or an ellipse. It is defined as the portion of the curve that lies between two distinct endpoints. An arc is named based on its endpoints, and it can be classified as a minor arc, major arc, or semicircle depending on its length. A minor arc is an arc that measures less than 180°, a major arc is an arc that measures more than 180°, and a semicircle is an arc that measures exactly 180°. The measure of an arc is typically given in degrees or radians, and it can be calculated using the formula:

measure of arc = (central angle/360) * 2πr

where r is the radius of the circle, and the central angle is the angle that the arc subtends at the center of the circle.

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Its CDF shows the probability of each value of X. is correct.

Probability is the measure of the likelihood that an event will occur. It is the ratio of the number of outcomes favorable to the event divided by the total number of possible outcomes. Probability is expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur.

The binomial distribution is a probability distribution that shows the probability of a success or failure outcome in an experiment that is repeated multiple times. Its PDF (probability density function) shows the probability of each possible value of X, and its CDF (cumulative density function) shows the probability of each value of X and all values of X less than it.

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Answer:

The function f(x) = -8t(t - 8) represents the height of the soccer ball at any given time t, where t is the time in seconds after the ball was kicked.

To find out how long the ball spends in the air, we need to determine the time at which the ball hits the ground. The ball hits the ground when its height is zero, so we can set f(x) = 0 and solve for t:

-8t(t - 8) = 0

This equation has two solutions: t = 0 and t = 8. The first solution corresponds to the time when the ball is kicked and the second solution corresponds to the time when the ball hits the ground. Since we're interested in the time the ball spends in the air, we need to subtract the time the ball was kicked from the time the ball hits the ground:

t = 8 - 0 = 8 seconds

Therefore, the ball spends 8 seconds in the air.

Answer:

-12x⁴-10x³+3x²+3x+2

Step-by-step explanation:

(3x²+x−2)(−4x²−2x−1)=3x²(−4x²−2x−1)+x(−4x²−2x−1)−2(−4x²−2x−1)

                                 { ( a+b ) ( a+b )=a ( a+b )+b ( a+b ) by distributive  property }

                                =  -12x⁴-6x³-3x²-4x³-2x²-x+8x²+4x+2

                                =   -12x⁴-10x³+3x²+3x+2  

The answer is A. The game is strictly determined and the value of the game is -7.

A rectangular array of characters, numbers, or phrases arranged in rows and columns is known as a matrix.

Given matrix, where we have to find out, is the game strictly determined for the following matrix or not?

[tex]\left[\begin{array}{ccc}-7&7&-3\\3&8&6\\1&3&-3\end{array}\right][/tex]

Using the minimax theorem, we know that if the game is strictly determined, the value of the game is equal to the value of the saddle point. If the game is not strictly determined, the value of the game may not exist or may be a range of values.

We can check each row and column for minimum and maximum values:

The minimum value in the first row is -7.

The maximum value in the second column is 7.

The minimum value in the third row is -3.

We can see that the element in the first row and second column is both the minimum in its row (-7) and the maximum in its column (7), so it is a saddle point. Therefore, the game is strictly determined and the value of the game is -7.

The answer is A. The game is strictly determined and the value of the game is -7.

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The trigonometry ratio that would be used to find a and x is 13. Sine and 14. Tangent.

The right triangle is the foundation of trigonometry. Hence, one of the relationships in that right triangle is defined by the tangent. The ratio of the opposing side to the adjacent side of a specific right triangle angle is the connection that the tangent specifies. You must first identify the hypotenuse in order to find the tangent. The hypotenuse is generally the longest side of the right triangle. After labelling your sides, you proceed to take the proper ratio.

The value of a is opposite to the given angle.

Here, the value of hypotenuse is also known.

Hence, the trigonometric identity that gives the relationship between opposite side and hypotenuse is sine. Option A is the correct answer.

14. For the triangle the segments are opposite side and adjacent side to the given angle.

Hence, the trigonometric identity that gives the relationship between opposite side and adjacent side is tan. Option C is the correct answer.

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By answering the presented question, we may conclude that This equation equation demonstrates that 36 equals the result of multiplying 3 by 12.

A math equation is a technique that links two assertions and denotes equivalence using the equals sign (=). In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For example, in the equation 3x + 5 = 14, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on either side of a letter. The logo and the programmed are usually interchangeable. As an example, 2x - 4 equals 2.  

The comparison "36 is three times as numerous as 12" may be written as follows:

36 = 3 x 12

This equation demonstrates that 36 equals the result of multiplying 3 by 12.

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The graph οf the equatiοn −7y + 5x = 5(−7 + x) is a straight line passing thrοugh the pοint (0, 5) with a negative slοpe.

A linear equatiοn in twο variables is an equatiοn that can be written in the fοrm ax + by = c, where a, b, and c are cοnstants and x and y are variables.

Tο graph the equatiοn −7y + 5x = 5(−7 + x), we can first find the x- and y-intercepts by setting each variable tο zerο in turn.

When y = 0, we get:

-7y + 5x = 5(-7 + x)

0 + 5x = 5(-7 + x)

5x = -35 + 5x

0 = -35

This is a cοntradictiοn, which means that there is nο x-intercept.

When x = 0, we get:

-7y + 5x = 5(-7 + x)

-7y + 0 = 5(-7 + 0)

-7y = -35

y = 5

Sο the y-intercept is (0, 5).

Therefοre, the graph οf the equatiοn −7y + 5x = 5(−7 + x) is a straight line passing thrοugh the pοint (0, 5) with a negative slοpe.

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We can use polynomial long division to find the remainder of the expression (5x^3 + 7x + 5) divided by (x + 2). The steps are as follows:

5x^2 - 3x + 19

       ____________

x + 2 | 5x^3 + 7x + 5

      - (5x^2 + 10x)

      ______________

              -3x + 5

              -(-3x - 6)

              ________

                    11

Therefore, the remainder of (5x^3 + 7x + 5) divided by (x + 2) is 11.

Answer:

The remainder of the polynomial equation is -49

Step-by-step explanation:

The conditional probability is given as follows:

P(B|A) = 1/2, option C.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The events are given as follows:

P(B|A) is the probability that the second digit is even, considering that the first digit was odd. As the digits cannot repeat, and there will be 8 remaining digits, out of which 4 will be even, the probability is given as follows:

P(B|A) = 4/8 = 1/2.

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Answer:

What are your goals for taking a gap year?

Are you looking to gain new experiences, skills, or perspectives?

Do you want to travel, learn a new language, or volunteer?

Are you trying to improve your mental health or overall well-being?

What are your current academic or career plans?

Do you have a clear idea of what you want to study or what career you want to pursue?

Have you already been accepted into a program or job?

What are your financial circumstances?

Can you afford to take a gap year without negatively impacting your future plans?

Do you have savings or a plan to work during your gap year?

How will taking a gap year affect your relationships with friends and family?

Will you be able to stay in touch with loved ones while you're away?

Will you miss any important events or milestones?

What are the potential risks and rewards of taking a gap year?

Could it delay your academic or career goals?

Could it help you gain valuable experience or clarity about your future plans?

How do you feel about the idea of taking a gap year?

Are you excited about the possibilities, or do you feel uncertain or anxious?

By answering these questions honestly, you should have a better idea of whether taking a gap year is the right decision for you. Keep in mind that there is no one-size-fits-all answer, and what works for one person may not work for another. Ultimately, the decision should be based on your own unique goals, circumstances, and desires.

Step-by-step explanation:

Check the picture below.

The length of the hypotenuse (x) in the given right triangle is approximately 10 units.

Hence the correct option is B.

Given is right triangle with perpendicular side having measurement of 5 units,

The acute angle between the base and the hypotenuse = 30°

The acute angle between the perpendicular and the hypotenuse = 60°

We need to find the length of the hypotenuse (x).

We can use the trigonometric ratio for sine (sin) to relate the lengths of the sides.

In this case, we'll use the sine of the 30° angle:

sin(30°) = opposite/hypotenuse

sin(30°) = 5/x

To solve for x, we can rearrange the equation:

xsin(30°) = 5

x = 5 / sin(30°)

Now, we can calculate the value of x using this equation:

x = 5 / sin(30°)

x ≈ 10 units

Therefore, the length of the hypotenuse (x) in the given right triangle is approximately 10 units.

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The triangle congruence postulate used for the given diagram is; SSS

There are different triangle congruency postulates namely:

SSS: Side Side Side Congruency Postulate

SAS: Side Angle Side Congruency Postulate

ASA: Angle Side Angle Congruency Postulate

AAS: Angle Angle Side Congruency Postulate

HL: Hypotenuse Leg Congruency Postulate

From the given image, we see that we see that we have three congruent sides shown of both triangles and as such the triangles are congruent by SSS Congruency Postulate.

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Answer:

First option, (4, -6)

Step-by-step explanation:

Scaled by 2. Multiply each coordinate of point C by 2.

(2*2, -3*2) = (4, -6)

Answer:

1.2 x 10^3 = 1,200

1.2 x 10^-2 = 0.012

1.2 x 10^2 = 120

1.2 x 10^-4 = 0.00012

Step-by-step explanation: