Translate the following to an algebraic expression: r squared minus the product of 6 and d plus 5

The complete sentence would be: "For 4x^(2)+6x+2=0, a=4, b=6, and c=2."

To complete the sentence, we need to identify the values of a, b, and c in the given equation. The equation is in the form of ax^(2)+bx+c=0, where a, b, and c are the coefficients of the respective terms.

Therefore, to fill in the blanks in the sentence, we can simply match the coefficients in the given equation with the corresponding letters:

a = 4, because the coefficient of the x^(2) term is 4
b = 6, because the coefficient of the x term is 6
c = 2, because the constant term is 2

So the complete sentence would be: "For 4x^(2)+6x+2=0, a=4, b=6, and c=2."

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1. The dimensions of A are 6 x 4.

2. The function is S could be onto, but it cannot be one-to-one.  (C)

1. This is because T: R4 → R6 is a matrix transformation that maps from a 4-dimensional space to a 6-dimensional space. Therefore, the matrix A must have 6 rows and 4 columns in order to be able to multiply with a 4-dimensional vector x and produce a 6-dimensional vector T(x).

2. This is because S: R3 → R2 is a matrix transformation that maps from a 3-dimensional space to a 2-dimensional space.

This means that there are more input vectors than there are output vectors, so it is not possible for S to be one-to-one. However, S could be onto if every vector in R2 can be obtained from some vector in R3 through the transformation S(x) = Bx.

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Using linear approximation, we estimate that ([tex]32.03^{4/5}[/tex]) is approximately equal to 31.952. It's important to note that this is only an estimate and may not be exact.

To estimate the value of  ([tex]32.03^{4/5}[/tex]) using linear approximation, we start by finding the differential of the function f(x) = [tex]x^{4/5}[/tex] at the point x = 32.

[tex]f(x) = x^{4/5}[/tex]

[tex]f'(x) = 4/5x^{-1/5}[/tex]

Evaluating [tex]f'(32)[/tex], we get:

[tex]f'(32) = (4/5)(32)^{-1/5} = 0.1585[/tex]

Now, using the linear approximation formula:

[tex]f(x) ≈ f(a) + f'(a)(x - a)[/tex]

where a is the point at which we are estimating the function, we have:

[tex]f(32.03) = f(32) + f'(32)(32.03 - 32)[/tex]

[tex]= 32^{4/5} + 0.1585(0.03)[/tex]

[tex]= 31.952[/tex]

Linear approximation is a useful tool for approximating values of functions near a given point, but it has limitations and may not work well for functions that are highly nonlinear or have discontinuities.

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Answer:

mean = 86

mean w/o 2 lowest = 92

median = 91

median w/o 2 lowest = 93

mode = 98

mode w/o 2 lowest = 98

Step-by-step explanation:

In a rhombus, all sides are equal in length, so we can write:

AB = BC = CD = AD

Let's use n to represent the length of any of the sides, such as AB. Then, we can write:

AD = AB

Therefore, the expression in terms of n to represent AD in rhombus ABCD is simply:

AD = n

The data set is not periodic, look at the graph below.

A relation R(x) is periodic with period T if:

R(x) = R(x + T)

For every value of x.

So the function has unique values in [0, T] tha are repeated in the interval [T, 2T] and so on.

Here we have a table with some data in it, and we want to see if it is periodic.

Now, wecan see that the number of cars goes up and down, so there may be a "period-like" behavior.

But the relation is clearly non-periodic.

Even if you graph the points you can see it, there is a pattern (for the grouping of the points) but it is not periodic.

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Answer:

not periodic

Step-by-step explanation:

They are correct took the test thank you for your help

Answer:

15=2.00x+1.50y

Step-by-step explanation:

In triangle ABC, measure of side BC or a is 8.8 unit

In trigonometry, the cosine rule states that the square of the length of any side of a given triangle is the sum of the squares of the lengths of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

cosA = (b² + c² - a²)/2bc

Given,

In triangle ABC

A = 49° , b = 10, c = 11

By cosine rule

cosA = (b² + c² - a²)/2bc

cos49° = (10² + 11² - a²)/2(10×11)

0.656 = (100 + 121 - a²)/220
144.32 = 100 + 121 - a²

a² = 221 - 144.32

a² = 76.68

a = √76.68

a = 8.7567 ≈ 8.8

Hence, 8.8 unit is measure of side a in triangle ABC.

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Answer: 1. x < 22       2. First option          3. x ≥ 5

Step-by-step explanation:

Closed dots means equal to or less/greater than.

Open dots means only less/greater than.

1. Open dot and arrow points left so x < 22

2. Only greater than so first option (Open dot and arrow points right)

3. Closed dot and arrow points right so x ≥ 5

Hope this helps!

In the given triangle, using congruency, ∠JHI is congruent to ∠SJT.

What is Triangle ?

Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.

In the given figure, we can see that there are two pairs of vertically opposite angles, which are opposite to each other at the intersection of two straight lines. These angles are:

According to the ASA Rule, triangles are congruent to one another if any two angles and the side between them are comparable to the corresponding angles and side. According to the AAS Rule, the triangle's angles and excluded side are equal in the same way.

In the given triangle, using congruency, ∠JHI is congruent to ∠SJT

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Answer:

The family will save $896 on airfare by vacationing to Vancouver

Step-by-step explanation:

Tickets to Fairbanks - $958 each (4 total people)

Total cost - 958 times 4 = $3832

Tickets to Vancouver - $734 each (4 total people)

Total cost - 734 times 4 = $2936

$3832 - $2936 = $896

The difference between the two points is a vertical displacement of 5 units downward from point T to point V.

The distance formula is used to calculate the distance between two points in a two- or three-dimensional coordinate system. It is derived from the Pythagorean theorem and involves finding the square root of the sum of the squares of the differences between the corresponding coordinates of the two points.

The difference between point T(9, -4) and point V(9, -9) is 5 units in the y-direction. Specifically, the y-coordinate of point V is 5 units less than the y-coordinate of point T. This can be expressed as:

V - T = (9, -9) - (9, -4) = (0, -5)

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Answer: G=(3, 4) R=(4, 8) A=(7, 8) M=(6, 4)

Step-by-step explanation:

translation is the movement of a point so 11 units right add 11 to the x value and 2 to the y value then do the opposite for going left and down

If Ella is 15 meters away from Mary and 9 meters away from Dante, then distance between Dante and Mary are 12 meters away from each other.

It is given that Ella is 9 meter away from Dante and in the Dante is in south of Ella. This means that if we consider a plane ground and mark the directions as north, south, east and west, Ella and Dante will be in north and south direction respectively. Since Mary is in the east direction of Dante, this means She will be in the South East direction of Ella and about 15 meters away from her. This creates a triangular connection between them.

Hence by applying the Pythagoras theorem, we get following equation:

ED^2 + DM^2 = EM^2

where,

ED = Distance between Ella and Dante

DM = Distance between Dante and Mary

EM = Distance between Ella and Mary

9^2 + DM^2 = 15^2

81 + DM^2 = 225

DM^2 = 144

DM = 12

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Step-by-step explanation:

Refer to pic...........

Answer:

(a) The probability that all 4 calls are for medical help can be calculated using the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where:

n is the number of trials (in this case, 4)

k is the number of successes (in this case, 4)

p is the probability of success on a single trial (in this case, 0.81)

Plugging in the values, we get:

P(X = 4) = (4 choose 4) * 0.81^4 * (1 - 0.81)^(4 - 4)

P(X = 4) = 0.5314

Therefore, the probability that all 4 calls are for medical help is 0.5314, rounded to 4 decimal places.

(b) The probability that at least 1 of the calls is not for medical help can be calculated using the complement rule:

P(at least 1 call not for medical help) = 1 - P(all 4 calls for medical help)

We already calculated the probability of all 4 calls being for medical help in part (a), which is 0.5314. So, using the complement rule, we get:

P(at least 1 call not for medical help) = 1 - 0.5314

P(at least 1 call not for medical help) = 0.4686

Therefore, the probability that at least 1 of the calls is not for medical help is 0.4686, rounded to 4 decimal places.

(c) The calculation in part (a) may not be valid if we choose 4 consecutive calls to the station because the 4 consecutive calls being medical may not be independent events. For example, if a large accident or a natural disaster occurs in the area, there may be a higher probability of multiple consecutive medical calls due to the same incident or cause. In that case, the assumption of independence between the events would not hold, and the binomial probability formula would not be applicable.

Step-by-step explanation:

Answer: (0, 48)

Step-by-step explanation:

To find the y-intercept, plug the x and y values in the equation y = -3x + b, and leave the b the same.

I will use (11, 15)

15 = -3(11) + b

15 = -33 + b

48 = b

The y-intercept is (0, 48)

Equation is y = -3x + 48

Hope this helps!

(a) The function combination (f + g)(x) is equal to x² - 3x + 12 and its domain are all real numbers.

(b) The function combination (f - g)(x) is equal to x² - 5x - 12 and its domain are all real numbers.

(c) The function combination (fg)(x) is equal to x³ + 8x² - 48x and its domain are all real numbers.

(d) The function combination (gf)(x) is equal to x³ + 8x² - 48x and its domain are all real numbers.

(a) To find the expression or value of the function combination (f + g)(x), we need to add f(x) and g(x).

(f + g)(x) = f(x) + g(x) = x² - 4x + x + 12 = x² - 3x + 12

Domain of (f + g)(x) : All real numbers

(b) To find the expression or value of the function combination (f - g)(x), we need to subtract g(x) from f(x).

(f - g)(x) = f(x) - g(x) = x² - 4x - (x + 12) = x² - 5x - 12

Domain of (f-g)(x) : All real numbers


(c) To find the expression or value of the function combination (fg)(x), we need to multiply the two functions.

(fg)(x) = f(x) * g(x) = (x² - 4x) (x + 12) = x³ + 8x² - 48x

Domain of (fg)(x) : All real numbers


(d) The function combination (gf)(x) is the same as (fg)(x).

(gf)(x) = g(x) * f(x) = (x + 12) (x² - 4x) = x³ + 8x² - 48x

Domain of (gf)(x) : All real numbers


In all cases, the domain is all real numbers because there are no restrictions on the values of x that can be used in the functions.

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Answer:Given that y represents the cost, and x represents the number of classes, to complete the statements, the table is given for Gymnastics while the equation, y = 18x + 20 is given for Ice-skating program.

Since the table already shows the cost for each specific number of classes for Gymnastics, find that of Ice-skating program for 1, 2, 3, and 4 classes.

For 1 class, substitute x = 1 into y = 18x + 20:

y = 18(1) + 20

y = $38

For 2 class, substitute x = 2 into y = 18x + 20:

y = 18(2) + 20

y = $56

For 3 class, substitute x = 3 into y = 18x + 20:

y = 18(3) + 20

y = $74

For 4 class, substitute x = 4 into the equation y = 18x + 20:

y = 18(4) + 20

y = $92

From the above, we can conclude that, Gymnastics is less expensive when the classes is 1.

Ice-skating is less expensive  when the classes is 3 or 4.

Step-by-step explanation:

From the given function, When the number of classes is 1 the football is less expensive.

When the number of classes is 1, the basketball is less expensive.

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Four main categories can be used to classify different sorts of functions. dependent upon element Function is a one-to-one relationship, a many-to-one relationship, onto function, one-to-one and into function.

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Answer:

The notation f⁻¹(-3) refers to the value(s) of x for which f(x) = -3.

However, the function f is not given in the prompt. Therefore, we cannot determine the value(s) of x for which f(x) = -3 or find f⁻¹(-3) without knowing the definition of f.

Step-by-step explanation:

The profit for buying pencils for $2 each and selling them for $2.40 is $6.40 and there is no loss.

The profit is the difference between the selling price and the cost price of the pencils. In this case, the profit per pencil is $2.40 - $2 = $0.40.

Since the total sales amount is $40, the number of pencils sold is $40/$2.40 = 16.67, which we can round down to 16 pencils. Therefore, the total profit is 16 * $0.40 = $6.40.

There is no loss in this scenario, as the selling price is higher than the cost price. Loss occurs when the selling price is lower than the cost price.

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The little monsters will do an overhead press and a squat at the same instant 3 times during the drill.

The process of calculating a value using operands and a math operator is referred to as a "operation" in mathematics. The math operator's symbol has predetermined rules that must be obeyed for the provided operands or integers. The five fundamental operations in mathematics are addition, subtraction, multiplication, division, and modular forms.

The prime factorizations of 12 and 30 are 2² x 3 and 2 x 3 x 5, respectively.

Hence, 2² x 3 x 5 = 60 is the smallest common multiple of 12 and 30.

This means that the little monsters will do an overhead press and a squat at the same instant every 60 seconds.

To find out how many times this will happen during the 200-second drill, we can divide 200 by 60:

200 ÷ 60 = 3 remainder 20

This means that there will be 3 complete cycles of both exercises during the 200-second drill, with an additional 20 seconds left over.

Therefore, the little monsters will do an overhead press and a squat at the same instant 3 times during the drill.

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Based on the data showing the ordered pairs of a linear function, we can find the slope of the line, which will be: 2.4. The closest correct option is letter c.

We need to use the following formula to find the intended result:

Slope = (change in y) / (change in x)

To calculate slope, we can pick any two points from the table. Choosing the points (0, -9) and (10, 15) we have:

Therefore, using two points from the table, we find that the slope of the line is 2.4. The option c) 2.1 is the closest to the result.

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The original number would be 3.

An equation is an expression that shows the relationship between two or more numbers and variables.

Consider that the 10s digit = x

And the units digit = y

x +y = 11                                  

The Sum of the digits = 11

10x + y + 45 = 10y + x            

Then Reversed number is 45 more  than original,

10x - x + y + 45 = 10y              

9x + y + 45 = 10y                    

9x + 45 = 10y - y                    

9x + 45 = 9y

Now, Put x +  y = 11 into the equation just found.

9x + 45 = 9(11 - x)                    

x + 45/9 = 11 - x                      

2x + 5 =     11                          

2x = 11 - 5

2x = 6                                      

x = 6/2

x = 3

Therefore, we have;

x + y = 11

3 + y = 11        

y = 11 - 3

y = 8

Henece, we can conclude that the original number is 38 and the new number is 83 which the digits are reversed.

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Answer:

Step-by-step explanation: 1. Down

2. Claire's line would go higher because she began further away from her house.

3. The lines would have the same slope , since they are going the same speed.

The number line that shows the solution to the inequality y - 2 < -5 is:

A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded.

What is inequality?

In mathematics, an inequality is a statement that compares two values, expressing that one value is less than, greater than, or less than or equal to, greater than or equal to, or not equal to another value.

The inequality is y - 2 < -5.

To graph the solution on a number line, we start by marking the point where y - 2 equals -5, which is y = -3. Then, since the inequality is less-than, we use an open circle to represent the point y = -3.

Next, we shade all the values of y that make the inequality y - 2 < -5 true. Since y is less than -3, we shade everything to the left of the open circle.

Therefore, the number line that shows the solution to the inequality y - 2 < -5 is:

A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded.

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The maximum possible height for the fish tank is  23.749 inches

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

We need to convert the tank capacity from gallons to cubic feet since we know the conversion factor of 1 cubic foot of water = 7.48 gallons:

Tank capacity = 100 / 7.48 cubic feet

= 13.369 cubic feet

Volume of fish tank = Length x Width x Height

= 54 inches x 18 inches x Height

= 972 inches³ x Height

The maximum possible height of the fish tank

Volume of fish tank = Tank capacity

972 cubic inches x Height = 13.369 cubic feet

Height = 13.369 cubic feet / 972 cubic inches

= 0.013753 cubic feet / cubic inches

To convert cubic feet to cubic inches, we multiply by 1728

Height = 0.013753 x 1728

= 23.7488 cubic inches / inch³

Hence, the maximum possible height for the fish tank is  23.749 inches

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We have shown that a line L is tangent to a circle C at a point P if and only if L is perpendicular to the line OP.

A line L is said to be tangent to a circle C at a point P if and only if L meets C at P and at no other point besides P. Given a circle centered at a point O, a point P on the circle, and a line L passing through P, we can show that L is tangent to the circle at P if and only if L is perpendicular to the line OP.

Let us assume that L is perpendicular to OP. Then, since L is perpendicular to the radius at P, it is also perpendicular to the circumference of the circle at P. This means that the line L only meets the circumference of the circle at the one point P, and so L is tangent to the circle at P.

Conversely, let us assume that L is tangent to the circle at P. This implies that the line L only meets the circumference of the circle at the one point P. Thus, since the line L must pass through the point P, it must be perpendicular to the line OP.

Therefore, we have shown that a line L is tangent to a circle C at a point P if and only if L is perpendicular to the line OP.

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This is a between-subjects study. The independent variable is the type of medication given. The dependent variable is the participants' blood pressures. The experimenters reported a p-value (Sig.) Based on Mean (top row) of 0.071. No, this is not statistic significant. No, we don't want a significant p-value for the Levene’s Test. This p-value of 0.071 indicates that the variance in the three groups is not significantly different.

1.

a. The p-value (Sig.) Based on Mean (top row): 0.071
b. This p-value indicates that the null hypothesis cannot be rejected, meaning that there is no significant difference between the three groups.
c. The Levene’s Test does not require a significant p-value for the data to be valid.
d. This p-value indicates that there is no significant difference in the variance between the three groups.

2. This is a between-subjects study.
Independent Variable: Dosage of HyBlox (high dose HyBlox, low dose HyBlox, or placebo sugar pill)
Dependent Variable: Blood Pressure on a continuous scale

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Instead of 200 participants aged 20 to 40, the research would need to unitary method include 100 young and 100 elderly people. One possible change would be to divide the sample into age groups.

The unit technique is a strategy for addressing issues that entails first figuring out the value of a single unit, then multiplying that value to figure out the needed value. Simply expressed, the unit technique is used to extract a single unit value from a multiple that is provided. For example, 40 pens would cost 400 rupees, which is equal to the cost of one pen.

Part A:

A randomized controlled trial would be the ideal approach for the new investigation (RCT). A control group and an experimental group should both be included in the study.

The Visual Analog Scale is a pain scale that may be used by participants to self-report their level of pain, which is one of the variables that should be measured (VAS). Functional status, quality of life, and unfavorable treatment effects are other factors that might be assessed.

Part B:

Instead of 200 participants aged 20 to 40, the research would need to include 100 young and 100 elderly people. One possible change would be to divide the sample into age groups.

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