If A=B and B=C, which property let's us say A=C?

The quadratic equation that models the fuel efficiency of the car is given by:

y = -0.01(x - 55)² + 32.

The equation of a quadratic function, of vertex (h,k), is given by the following rule:

y = a(x - h)² + k

In which the parameters of the equation are described as follows:

For a certain model of car the fuel efficiency is maximized at 32 miles per gallon with a speed of 55 mph, hence the vertex is given by:

(h,k) = (55,32).

Hence the rule is:

y = a(x - 55)² + 32

When x = 65, y = 31, hence we can find the leading coefficient a as follows:

31 = a(65 - 55)² + 32

100a = -1

a = -0.01.

Hence the equation is given by:

y = -0.01(x - 55)² + 32.

The problem is incomplete, hence we suppose that it asks for the quadratic model of the car's fuel efficiency.

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The equation is  1068.50 + 37.75 x =  1672.50 and the value of x is 16.

Members of our lacrosse team raised 1672.50 to go to a tournament.

Amount raised by lacrosse team = 1672.50

Let the number of players in lacrosse team = x

They rented a bus for 1068.50 and budgeted $37.75 per player for meals. So, mathematically this can be represented as

1068.50 + 37.75 x

Total amount paid by lacrosse team =  1068.50 + 37.75 x

As amount raised by lacrosse team and the amount paid by lacrosse team are equal so we can write

1068.50 + 37.75 x =  1672.50

37.75 x =  1672.50 - 1068.50

37.75 x =  604

x = 16

Thus, we can conclude that the value of x is 16 and the equation is 1068.50 + 37.75 x =  1672.50.

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[tex]5.51134751094269\times10^8[/tex] transistors could fit on a microchip [tex]19[/tex] years later.

Moore's law predicts that the number of transistors that can be fit on a microchip will increase 40% every year.

So the expected increment every year [tex]40\%[/tex].

Microchips from a given year could hold about [tex]922,200[/tex] transistors.

We have to find ow many transistors could fit on a microchip [tex]19[/tex] years later.

From the question total years are [tex]19[/tex].

Since the number of transistors is increased every year so number of transistors of previous year added. So we can see that  the number of transistors that can be fit on a microchip is increased compound. We can find the total number of transistors by multiplying number of transistors with the rate assembled by one. So we can use the formula

So the number of transistors could fit on a microchip 19 years later.

Number of transistor = Microchips from a given year could hold about transistors(1 + increment rate)^total years

Number of transistor [tex]=922,200(1+\frac{40}{100})^{19}[/tex]

Number of transistor [tex]=922,200(1+\frac{2}{5})^{19}[/tex]

Number of transistor [tex]=922,200(\frac{5+2}{5})^{19}[/tex]

Number of transistor [tex]=922,200(\frac{7}{5})^{19}[/tex]

After evaluating the expression using the calculator we get

Number of transistor [tex]=551134751.094269[/tex]

Number of transistor [tex]=5.51134751094269\times10^8[/tex]

Hence, [tex]5.51134751094269\times10^8[/tex] transistors could fit on a microchip [tex]19[/tex] years later.

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Leah can run 320 yards in 2 minutes at the same rate as she can run 720 yards in 4.5 minutes. The correct option is B. 320.

To find out how many yards Leah can run in 2 minutes at the same rate, we can use the concept of proportionality.

Let's set up a proportion based on the information given:

720 yards / 4.5 minutes = x yards / 2 minutes

To find the value of x, we can cross-multiply:

4.5 minutes × x yards = 720 yards × 2 minutes

Now, divide both sides by 4.5 to solve for x:

x yards = (720 yards × 2 minutes) / 4.5 minutes

x yards = 320 yards

So, Leah can run 320 yards in 2 minutes at the same rate.

The correct answer is B. 320.

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We have a rectangular slab.

The volume of concrete is equal to the volume of this rectangular prism.

The volume of this prism is equal to the product of its length, width and thickness.

Then, we can write:

We convert the thickness from inches to feet by multiplying it by a unit ratio 1 ft / 12 inches, which has a value of 1, as 1 ft = 12 inches, but let us change the units from inches to feet.

When we have all the measures in feet we can have the volume in cubic feet.

Answer: 232 cubic feet.

There are 16 half-cup servings of beans and 4, three-ounce servings of shrimp.

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

Let x represents number of half-cup servings of beans

Let y represents  number of 3 ounce servings of shrimp  

We have a system of equations, one for carbs and one for calories;

7x + 9y = 150

30x + 190y = 1400  

Now,

30(7x + 9y) = 30(150)  

-7(30x + 190y) = -7(1400  )  

210x + 270y = 4440  

-210x - 1330y = -8680

-1060y = -4240  

y = 4

Then substitute we get;

7x + 9y = 150

7x + 9(4) = 150

7x + 36 = 150

7x =  112

x = 16

Hence; X = 16 and Y= 4

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I will plug in the POINTS including k in the equation each point in its place either x or y.

[tex]( - 2)^{2} +( {k})^{2} = 20 \\ 4 + {k}^{2} = 20 \\ k^{2} + 4 - 20 = 0 \\ {k}^{2} - 16 = 0 \\ (k + 4)(k - 4) = 0 \\ \\ k + 4 = 0 \\ \\ or \\ \\ k - 4 = 0 \\ \\ k = 4 \\ or \\ k = - 4[/tex]

ATTACHED IS THE SOLUTION

for the function

f(x) = (x -g)(x - h)

To get the x-intercept, we can equate the function to zero

f(x) = (x -g)(x - h) = 0

so (x - g) = 0

which gives x = g

And (x - h) = 0

which gives x = h

Since we have been told that g and h are positive, then it follows that both intercepts are positive

[tex]\begin{cases} f(x)=3x-1\\\\ (f\circ g)(x) = x^2 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ (f\circ g)(x)\implies f( ~~ g(x) ~~ )~~ = ~~3( ~~ g(x) ~~ ) - 1\implies \stackrel{(f\circ g)(x)}{x^2}~~ = ~~3g(x)-1 \\\\\\ x^2+1=3g(x)\implies \cfrac{x^2+1}{3}=g(x)[/tex]

Answer:

x = 14 and y = 42

Step-by-step explanation:

From the two entries that have both the numbers od adults*A) and students(S) we find a ratio of S/A to be 7 for both cases.  We'll make the assumption that is the same ratio in the two cases involving x and y.

To find x and y, multiply the number of adults by 7 to find the number of students,

x = 14 and y = 42

A      S    Ratio S/A = 7

1 7      7

2 x     14

4 28    28

6 y    42

The answer is FALSE. The likelihood of discovering a substantial difference between treatments does not increase with any factor that makes treatments more variable.

In experiments, you create situations where several treatments (such a are used in order to investigate the impact of an independent variation.

Every participant in a between-subjects or between-groups design only experiences one condition, and group differences between participants in various conditions are compared. In contrast, no participant in a within-subjects design is exposed to every condition.

As a result, the likelihood of discovering a substantial difference between treatments is not increased by factors that enhance variation within treatments.

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The rate of change of the given relation is 1.7142 the value of y is 36 centimeters.

The rate of change is the change of a quantity over 1 unit of another quantity.

Most of the time the rate of change is the change with respect to time.

As per the given question,

The water level rises 12 centimeters every 7 minutes.

0 minutes → 0 cm

7 minutes → 12 cm

14 minutes → 24 cm

21 minutes → 36 cm.

Since, (21,y) best match with the above condition.

So, 21 minutes is the time taken while 36 cm is the level of water.

Slope or rate of change = 12/7 cm/minutes.

And, 36/21 = 12/7 (proved)

Hence "The rate of change of the given relation is 1.7142 the value of y is 36 centimeters".

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The online shopping site would sell 756000 items in 30 minutes

Given

The online site would sell 420 items in a second

To find number of items it would sell in 30 minutes first of all convert minutes into seconds and continue to solve the problem.

To convert minutes into seconds just multiply minutes with 60.

because one minute is equal to 60 seconds.

Therefore 30 minutes = 30 x 60 seconds

30 minutes = 1800 seconds

Say the number of items sold by sire in 30 minutes be x.

now according to the condition in equation

420 x 1800 = x

x= 756000

Hence the site will sell 756000 items in 30 minutes.

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If line m is parallel to line n then determine the value of x= 65°

2x+50° = 180°

2x = 180° - 50°

2x = 130°

x = 130°÷2

x = 65°

Parallel lines are  lines that do not cross or meet  at any point in the plane. They are always parallel and  equidistant from each other. Parallel lines are non-intersecting lines. We can also say that parallel lines meet at infinity.

Properties of Parallel Lines

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The value of x is 25. It states that when two parallel lines are cut by a transversal, the resulting alternate interior angles or alternate exterior angles are congruent.

Parallel lines are coplanar straight lines that do not intersect at any point in geometry. Parallel planes are planes that never meet in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance.

Parallels, paralleling, and paralleled are all word forms. a countable noun A parallel is something that is similar to something else but exists or occurs in a different place or at a different time.

Parallel lines are lines that are always the same distance apart in a plane. Parallel lines never cross. Perpendicular lines are those that intersect at a right angle (90 degrees).

Two different interior angles.

- (2x - 10)°

- (65 - x)°

Because lines m and n are parallel and because of the alternate angles theorem.

We can see that.

2x - 10 = 65 - x

2x + x = 65 + 10

3x = 75

x = 75/3

x = 25

Hence, the value of x is 25.

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The actual closet has a length of 6 feet

The scale of the drawing is given as

Scale = 8 inches : 3 feet.

Also, we have the length of the closet to be

Length = 16 inches

So, we have

16 inches : Actual length = 8 inches : 3 feet.

Multiply the ratio by 2

So, we have

16 inches : Actual length = 16 inches : 6 feet.

By comparison, we have

Actual length = 6 feet

Hence, the length of the actual closet is 6 feet

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[tex]\frac{v}{8} -3.1=-15.9[/tex]

Simplify equation:

[tex]\frac{1}{8}v+-3.1=-15.9[/tex]

[tex]\frac{1}{8} v-3.1=-15.9[/tex]

Add 3.1 to both sides:

[tex]\frac{1}{8} v-3.1+3.1=-15.9+3.1\\[/tex]

[tex]\frac{1}{8} v=-12.8[/tex]

Multiply both sides by 8:

[tex]8\times(\frac{1}{8} v)=(8)\times(-12.8)\\-102.4[/tex]

[tex]\fbox{v=-102.4}[/tex]

Answer:

A is correct.

[tex]g = \frac{p}{6} - 15[/tex]

Step-by-step explanation:

[tex]p = 6g + 90[/tex]

[tex]6g = p - 90[/tex]

[tex]g = \frac{p}{6} - 15[/tex]

So A is correct.

Although part of your question is missing, you might be referring to this complete question "Translate the sum of m and 2.33 multiplied by s is 77.77 into an algebraic equation. Do not solve the equation."

Translated equation is m + 2.33s = 77.77

An algebraic equation is the equality of two expressions formulated by applying a set of variables such as addition, subtraction, multiplication, division, raise to power, etc. The phrase " the sum of a and b" into an algebraic expression is determined as a+b. It deals with symbols and these symbols deal with each other through variants.

Hence, the equation translated is a linear equation of algebraic equations.  m+ 2.33s = 77.77

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Answer:

[tex]f(x)=x^2+9x+4+\dfrac{9}{x-4}[/tex]

Step-by-step explanation:

Long Division Method of dividing polynomials

Given:

[tex]\textsf{Dividend: \quad $x^3+5x^2-32x-7$}[/tex]

[tex]\textsf{Divisor: \quad $x-4$}[/tex]

[tex]\large \begin{array}{r}x^2+9x+4\phantom{)}\\x-4{\overline{\smash{\big)}\,x^3+5x^2-32x-7\phantom{)}}}\\{-~\phantom{(}\underline{(x^3-4x^2)\phantom{-b))))))..)}}\\9x^2-32x-7\phantom{)}\\-~\phantom{(}\underline{(9x^2-36x)\phantom{)))..}}\\4x-7\phantom{)}\\-~\phantom{()}\underline{(4x-16)\phantom{}}\\9\phantom{)}\\\end{array}[/tex]

Therefore:

[tex]f(x)=x^2+9x+4+\dfrac{9}{x-4}[/tex]

Definitions

Dividend: The polynomial which has to be divided.

Divisor: The expression by which the divisor is divided.

Quotient: The result of the division.

Remainder: The part left over.

Answer:

15 ft

Step-by-step explanation:

5:8

?:24

8x3=24    SO    5x3=15

Given that 3 unit factor growth is 1.65

Then 1 unit growth factor = (1.65)^1/3 = 1.181

2 unit growth factor of F  = 1.396

And 1/2 unit growth factor = (1.65)^0.5/3 = (1.65)^0.53/3 = (1.65)^1/6

                                              = 1.0875

or 1/2 unit growth of factor f = 1.0875

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All real numbers r for which there exists exactly one real number a such that when (x+a)(x² +rx+1) is expanded to yield a cubic polynomial, all of its coefficients are greater than or equal to zero are given as r = -1

A real number is a quantity of a continuous number that can express a distance along a line in mathematics.

Hence the workings for the above result are indicated as follows:

Expanding the brackets, we see that we want the following three inequalities to be true.

a ≥ 0 (constant term)         (1)

ar + 1 ≥ 0 (coefficient of x) (2)

a + r ≥ 0 (coefficient of x²) (3)

If r ≥ 0, then any a ≥ 0 meets the requirement of (1), (2), and (3).

It remains to address r < 0. In this case, note that (3) immediately suggests (1)  


Hence, we only need to look at (2) and (3). Given that r < 0, inequalities (2) and (3) are equivalent to the following.

a ≤ − 1/r                        (4)

a ≥ − r                           (5)

Therefore, we seek all values of r < 0 such that there is exactly one real number satisfying the expression −r ≤ a ≤ −1/r                 (6)

Thus −r = −1/r ,

This implies r = ±1.

Given that r < 0 we have r = −1.

This implies that the only corresponding value of a is a = 1.

It only remains to follow that (x + 1)(x² − x + 1) = x³ + 1, which has no negative coefficients.

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Full Question:

Find all real numbers r for which there exists exactly one real number a such that when (x+a)(x² +rx+1) is expanded to yield a cubic polynomial, all of its coefficients are greater than or equal to zero.

The ratio of the volume of the large sphere to the volume

of the small sphere is 1226 .

V = 4/3 r³ is the equation to calculate a sphere's volume. The volume of a sphere is calculated using the following formula: 4/3rds of Pi and the cube of the sphere's radius. A sphere is a geometrical object that is a three-dimensional equivalent of a two-dimensional circle . A sphere is a collection of points in three-dimensional space that are all located at the same r distance from a particular point. The radius of the sphere is equal to r, and the provided point is its center. In the works of the ancient Greek mathematicians, spheres are first mentioned.

In several branches of mathematics, the sphere serves as a basic building block. Also found in nature and industry are spheres and nearly-spherical shapes.

Volume sphere = 4/3πr³

Volume of sphere 1

D = 4 inches

r = 2 inches

So,

Volume = 4/3π(2)³

= 33.51 inches³

Volume of sphere 2

D = 428 inches

r = 214 inches

So,

Volume = 4/3π(214)³

= 4.11 ×[tex]10^{7}[/tex] inches³

Ratio

= sphere 2: sphere 1

= 4.11 ×[tex]10^{7}[/tex] : 33.51

= 1226

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The height of the wall in feet is 2.5 feet.

According to the question,

We have the following information:

The number of bricks, B , needed to build a wall of length L feet and uniform height H feet can be found by the equation B = 7 L H .

A wall of uniform height that is 16 feet long is constructed using 280 bricks.

So, we have:

B = 280 and H = 16

Putting these values in the given expression:

B = 7LH

280 = 7*L*16

L = 280/(7*16)

L = 280/112

L = 2.5 feet

Hence, the height of the wall in feet is 2.5 feet.

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Solution of the given algebraic expression (f-g)(x) is equal to 4x³+6x²-7x-1

Algebraic equations are defined as mathematical statements in which two algebraic expressions are set equal to each other. An algebraic expression usually consists of  variables,  coefficients and  constants. Algebraic equations can be of many types, such as monomial algebraic equations, binomial algebraic equations, quadratic algebraic equations, polynomial equations.  

Given in the question that the value of f(x) is equal to 4x³+6x²-3x-4

and the value of g(x) is equal to 4x-3.

Subtracting g(x) from f(x) we get,

(f-g)(x)= 4x³+6x²-3x-4-4x+3

4x³+6x²-7x-1

Therefore, solution of the given algebraic expression (f-g)(x) is equal to 4x³+6x²-7x-1.

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The percentage profit for the so is that were made is 40.32%.

From the information, Rowena buys cashmere wool in 20g balls. Each ball of cashmere wool costs her £1.42 and she pays her sister £8 to knit each pair of socks. The cost will be:

= (£1.42 × (20 + 135) + (40 × £8)

= £220.1 + £320

= £540.1

The selling price will be:

= £18.95 × 40

= £758

Therefore, the percentage profit will be:

= Profit / Cost price × 100

= (758 - 540.1) / 540.1 × 100

= 217.9 / 540.1 × 100

= 40.32%

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