Given f(x) = -(x - 5)^2 + 1, what is the value of a?

The polynomial's zeros must be located using a method of your choice, and the linear expressions that produce those zeros must then be combined in order to describe the polynomial as a product of linear factors.

The term "triple zero" or "zero with multiplicity 3" is used to describe this. The power p governs the behaviour close to the x-intercept if a polynomial has a factor of the type (xh)p. A zero of multiplicity p is defined as x=h. The x-axis will be touched at zeros with even multiplicities on a polynomial function's graph.

A real number is multiplied by an imaginary unit, I whose feature i2 = 1 defines it as an imaginary number. Bi is an imaginary number, while b2 is its square. For instance, the square of the fictitious integer 5i is 25. Zero is regarded as both real and fictitious by definition.

You must first determine the polynomial's zeros using the method of your choice, and then combine the linear equations that result in those zeros. If you factor, you will arrive at the third degree polynomial, which must then be sorted through.

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Answer:

-------------------------------

Slope- intercept form:

Use two points on the line:

The first point is the y- intercept:

The slope is:

The line is:

Answer:

x intercepts (-2,0) and (-4,0)

y intercept: (0,8)

Vertex: (-3,-1)

Axis of symmetry x = -3

Step-by-step explanation:

Answer:

A) 270

Step-by-step explanation:

Interest = principle x time x rate

Interest = 3000 x 2 x .045   4.5% = .045 as a decimal

Interest = 270

The best estimate willl 20

Step-by-step explanation:I

The solution to the equation 7x² - 10 = -17 is x = i

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

7x^2-10=-17

Express the equation properly

So, we have the following representation

7x² - 10 = -17

Add 10 to both sides of the equation

This gives

7x² = -7

Divide both sides by 7

x² = -1

Take the square roots

x = √-1

Rewrite as

x = i

Hence, the solution is x = i

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The statement about probability that is true is that the probability of landing on purple is equal to the probability of landing on yellow. That is option D

Probability is defined as the possible outcome of an event which may likely or unlikely occur.

The total number of sections with different colours = 8

Sections 1 and 8 are purple.

Sections 2 and 3 are yellow.

Sections 4, 5, and 6 are blue.

Section 7 is orange

The probability of landing on purple is equal to the probability of landing on yellow. That is;

probability of landing a purple = 2/8 = 1/4

Probability of landing a yellow = 2/8 = 1/4

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The relationship between the green highlighted segment in triangle 2 and the blue highlighted segment in triangle 1 is D. The highlighted segments are congruent.

Congruent segments are segments in different shapes that have the same length and angle. In other words, they are identical to each other even though they are in different shapes.

The green highlighted segment in triangle 2 and the blue highlighted segment in triangle 1 are congruent segments because the blue highlighted segment was segment the green highlighted segment was derived from which is why they are the same.

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The given function expressions is  24f + 14g

Given,

-3 × f (-8) + 7 × g(2)

= -3f (-8) + 7g (2)

Simplifying the above equation,

= -3f (-8) = 24f

= 7g (2) = 14g

Then we get,

= 24f + 14g

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Answer:

a)  See below.

b)  Geometric sequence

[tex]\textsf{c)} \quad a_n=7.5(0.5)^{n-1}[/tex]

Step-by-step explanation:

From inspection of the given table, t(n) halves each time n increases by 1.

Therefore:

[tex]\implies a_4=1.875 \div 2 = 0.9375[/tex]

[tex]\implies a_5=0.9375 \div 2 =0.46875[/tex]

Completed table:

[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} n&t(n) \\\cline{1-2} \vphantom{\dfrac12} 1& 7.5\\\cline{1-2} \vphantom{\dfrac12} 2& 3.75\\\cline{1-2} \vphantom{\dfrac12} 3&1.875 \\\cline{1-2} \vphantom{\dfrac12} 4& 0.9375\\\cline{1-2} \vphantom{\dfrac12} 5& 0.46875\\\cline{1-2} \end{array}[/tex]

As the given sequence has a constant ratio of 0.5, it is a geometric sequence.

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

The first term of the sequence is 7.5.  Therefore,:

The common ratio is 0.5. Therefore:

Therefore, to write an equation for the given geometric sequence, substitute the found values of a and r into the formula:

Answer:

[tex]\frac{19}{18}=1\frac{1}{18}[/tex]

Step-by-step explanation:

[tex]3\frac{1}{6}\div3=\frac{19}{6}\div3=\frac{19}{6}*\frac{1}{3}=\frac{19}{18}=1\frac{1}{18}[/tex]

By using the given relation, we can perform a change of units to get:

$2525 = 108,072.25 Ars.

Here we want to do a change of units, from US dollars to Argentine pesos.

We know the relation:

$0.023364 = 1 Ars.

Here we want to convert $2525 to argentine pesos, then we just need to divide by $0.023364

$2525 = ($2525/$0.023364) ars = 108,072.25 Ars.

That is the equivalent amount in Argentine pesos.

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a) To evaluate loga 15, we can use the property of logarithms that states logab = loga + logb. Since 15 = 3 * 5, we can use this property to find that loga 15 = loga 3 + loga 5. Since loga 3 = 0.56 and loga 5 = 0.83, we can add these values to find that loga 15 = 0.56 + 0.83 = 1.39.

The power to which a number must be increased in order to obtain additional values is referred to as a logarithm. The easiest approach to express enormous numbers is this manner.

Numerous significant characteristics of a logarithm demonstrate that addition and subtraction logarithms may also be represented as multiplication and division of logarithms.

b) To evaluate loga(2/5), we can use the property of logarithms that states log(a/b) = loga - logb. Since 2/5 = 2*(1/5) we can use this property to find that loga(2/5) = loga2 - loga(1/5). Since loga2 = 0.36 and loga(1/5) = -loga5, we can subtract these values to find that loga(2/5) = 0.36 - 0.83 = -0.47

c) To evaluate loga (8a^4), we can use the property of logarithms that states log (a^n) = nloga. We get, loga (8a^4)=loga 8 + log (a^4)

=> loga 8 + loga (a^4)

=>3loga 2 + 4 loga a

=>3loga 2 + 4

=>3 * 0.36 + 4

=5.08

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the total area will be covered in the paint will be 2143.9cm²

What is cylinder?

Two parallel, identical bases connected by a curving surface form a 3D solid shape known as a cylinder. Similar to a disc in shape, these bases. The axis of the cylinder shape is a line drawn through the middle of, or connecting, two circular bases. Perpendicular distance is the measurement separating the two bases, and it is denoted by the letter "h," which stands for height. The distance between the two circular bases' centers and outer edges is known as the cylinder's radius and is denoted by the letter "r". A rectangle and two circles combine to form the cylinder.

A cylinder with base radius of 4 cm and a height of 7 cm is removed from the cuboid.

Volume of cuboid is = 16*15*24 = 5760 cm³

Volume of the cylinder = π r² h = π* 4² *7 = 351.85 cm³

So the surface area of the cylinder = 2π r h = 2*π*4*7 = 175.9 cm²

Total area of the cuboid = 2(240+360+384) = 1968

Toatl area = 1968+175.9 = 2143.9cm²

So the total area will be covered in the paint will be 2143.9cm²

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Answer:

True

Step-by-step explanation:

True

Therefore , the solution of the given problem of expression comes out to be 4x² +1 cannot equal 0 and thus (4x²≥0+1) has no Real factors.

Verifying an algebraic expression requires substituting a number for each variable and performing arithmetic operations. Given that 6 + 6 equals 12, the answer variable in the example above is equivalent to 6. If we are aware of the values of the variables, we can substitute those values for the original ones, which will allow us to evaluate the expression.

Here,

It is important to note that now the ratio of a coefficient of the terms 

The coefficient ratio of the words

8x³ and 2x is 8:2 = 4:1, and the coefficient ratio of the phrases 12x² and 3 is 12:3 = 4:1.

This suggests that we should categorize the original statement as follows: 

This suggests that we should combine the original expression, which is written as

=> (8x³+2x)(12x²+3)=2x(4x²+1))3(4x²+1),

before determining the common component (4x2+1)=(2x³)(4x2+1).

The fact that 4x²≥0 for x ∈ R means that

4x² +1 cannot equal 0 and thus (4x²≥0+1) has no Real factors.

Therefore , the solution of the given problem of expression comes out to be 4x² +1 cannot equal 0 and thus (4x²≥0+1) has no Real factors.

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The value of dy when x changes from -1 to -1.1 for equation y = 4x² is 0.84.

Here we are given an equation y = 4x²

In an equation, dy/dx, implies the change in y due to a change in x.

Now here we already have given that x changes from -1 to -1.1.

Hence, here we need to find the values of y when x = -1 and when x = -1.1

Then we need to subtract the value of y when x = -1.1 and when x = -1

We are given y = 4x²

Hence when x = -1,

y = 4 X 1

= 4

When x = -1.1

y = 4 X 1.21

= 4.84

Hence dy = 4.84 - 4

= 0.84

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Answer:2

Step-by-step explanation:1+1=2

Answer: 2

Step-by-step explanation:

1

+

1

____

2

The equivalent function of the form J(t)= ab^t is J(t) = 448(16)^(t)

Equivalent functions are functions that work the same even though they look different. If two exponential functions are equivalent, then the two functions will have the same value when we substitute the same value(s) for the variable(s).

We can write the given function, (t)=28(4)^(2t+2) as:

J(t) = 28(4)^(2t+2)

J(t) = 28(4²)^(t) × 4²

J(t) = 28(16)^(t) × 16

J(t) = 448(16)^(t)

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In the graphic below, assuming the lines are parallel, the value of x is 15.

Parallel lines are coplanar infinite straight lines that do not cross at any point in geometry. Parallel planes are planes that never intersect in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance. Parallel lines in geometry are two lines in the same plane that are at equal distance from each other but never intersect. They can be both horizontal and vertical in orientation. Parallel lines can be found in everyday life, such as zebra crossings, notepad lines, and railway tracks.

Here,

6x+3=7x-12

x=15

The value of x in the figure below assuming that the lines are parallel is 15.

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The the average age of the remaining 4 students is 9.5 years.

The average may be calculated by dividing the total number of values by the sum of all the numbers. An average of the values in a sample of data may be used to determine a mean. In other words, the arithmetic mean is another name for an average. A mean is a term used to describe the average.

The average age of 5 students is 10 years.

∴  Sum of age of 6 students =5 × 10 = 66

⇒  When two more students of age 5 and 1 added to 4 students then, total students will become 8

⇒  Sum of age of 6 students =66 + 6 + 4 = 76

∴  Required average =

76 / 8  = 9.5

=9.5 years

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According to the line-plot Sofia needed 10(3/4) more feet of bricks.

What is the line-plot?

A line plot is a graph that shows data as checkmarks or dots across a number line, indicating the frequency of each value.

In the line plot the horizontal line is showing the values of the size in feet of the bricks say 'l'.

The number of vertically aligned crosses at a given value of  'l', indicates the length of bricks for which the 'l' is needed in the project.

Follow the formula - l × n (number of crosses) = total bricks in feet

0/4 × 0 = 0

1/4 × 2 = 2/4

2/4 × 4 = 8/4

3/4 × 3 = 9/4

1 × 6 = 6

To obtain the total size in feet add all the values -

L = 2/4 + 8/4 + 9/4 + 6

L = (2 + 8 + 9 + 24)/4

L = 43/4

L = 10(3/4)

Therefore, the feet of bricks required is 10(3/4).

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The store had $0 profit first in month 4 and then in month 10

The maximum profit of $1000 occurred in month 7

The function is given as

p(z) = -z² + 14z - 40

Next, we set p(z) = -z² + 14z - 40 = 0 and then solve for z.

So, we ha

-z² + 14z - 40 = 0

Rewrite as

z² - 14z + 40 = 0

Factorize

(z - 10)(z - 4) = 0

Solve for z

z = 10 and z =4

So the store had a profit of zero dollars in month 4 and then in month 10

Here, we calculate the vertex using

x = -b/2a = -14/2*-1 = 7

Plugging this value into the function, we get:

p(7) = -7² + 14*7 -40 = 49-98+40 = 1

so the maximum profit was $1000 and it occurs in the month 7.

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Answer: [tex]B. \frac{2}{7} -\frac{2}{k}[/tex]

Step-by-step explanation:

Reason:

Point C is located at (3,3)

Triple each coordinate since the scale factor is 3. That's how we go from (3,3) to (9,9)

If the scale factor was 5 for instance, then we'd go from (3,3) to (15,15)

This trick works only if the center of dilation is the origin.

Answer:

C' = (-3, 4)

Step-by-step explanation:

When a shape is dilated by a factor of 3, the size of the shape is multiplied by 3 in both the x and y directions. To find the new coordinates of point C' after a dilation by a factor of 3, we can multiply the original coordinates of point C by 3.

The original coordinates of point C are (-2, -10). When we multiply these coordinates by 3, we get (-6, -30) for the new coordinates of C' after the dilation. So the answer is (-6, -30)

The null hypothesis is true for an analysis of variance -MS (between) should be about the same size as MS within. Option (d) is the correct answer.

If the null is true, MS between and MS within should be about the same since they are both estimates of the same quantity (variance).

The null hypothesis is a characteristic arithmetic theory that suggests that no statistical relationship and significance exists in a set of given, single, observed variables between two sets of observed data and measured phenomena.

The null hypothesis in statistics defines that there is no difference between groups or no relationship between variables.

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He must get at least 97% on the final examination to earn an A in the course.

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Answer:

she had here eyes open for 12.4 more hours than she had them closed

Step-by-step explanation:

1/10 eyes closed = 9/10 eyes open

9/10 is 90% is 0.9

1/10 is 10% is 0.1

15 1/2 is 15.5

15.5 x 0.9 = 13.95

15.5 x 0.1 = 1.55

13.95-1.55 = 12.4

Therefore , the solution of the given problem of unitary method comes out to be $ 4 for garry  and $ 1.33 for peter.

To accomplish a task through using unitary procedure, multiply the number of a tiny slice by two after first determining its size. The unit technique, to put it simply, is used to isolated a programmed object from either a specific set or set of sets. For illustration, 40 pens would cost 400 pounds ($1.01), or Rs. It's feasible that one nation will have complete control over the technique used to do this. Almost all living things have a unique characteristic. It can integrate and reciprocate in equal measure (mathematics, algebra).

Here,

Given :

Garry charges for one carrot for  :

=> 12/3

=> $ 4

Peter charges for one carrot :

=> 20/15

=>  4/3

=> $ 1.33

Therefore , the solution of the given problem of unitary method comes out to be $ 4 for garry  and $ 1.33 for peter.

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The area of the irregular polygon is 24 square inches. Hence option A is the correct option.

What is an irregular polygon?

An irregular polygon does not have all of its sides equal, nor are all of its angles equal in size. Scalene triangles, right triangles, isosceles triangles, rectangles, parallelograms, irregular pentagons, irregular hexagons, and so on are examples of irregular polygons.

The length of DE is 5 in and HI is 5in.

The length of AL is 12in.

The length of AD + EH + IL = AL - (DE+HI) = 12 - (5+5) = 2 in

The length of AB = DC = EF = HG = IJ = LK = 7in.

The sum area of the rectangles ABCD, EFGH, and IJKL is

AB×AD + EF×EH + IJ×IL

= 7×AD + 7×EH +7×IL

= 7(AD + EH + IL)

= 7×2

= 14 square inches

The length of DW = EX = HY = IZ = 7 - 6 = 1in.

The area of DWXE is DW×WX = 1×5 = 5 square inches

The area of HYZI is HY×YZ = 1×5 = 5 square inches

The area of the irregular polygon is

14  + 5 + 5 square inches

= 24 square inches

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