Translate this sentence into an equation. 171 is the product of 9 and Chrissy's height.

The value of y when a = 1 and b = 2 is 22.

The equation of can be solved as follows: We will substitute the value of a and b  in the equation to find the value of y.

Therefore,

y = 3ab + 2b³

Let's find y when a = 1 and b = 2

Hence,

y = 3(1)(2) + 2(2)³

y = 6 + 2(8)

y = 22

Therefore,

y = 22

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Answer:

d

Step-by-step explanation:

Answer:

Factorise 18a²y - 27ay

=9ay(2a-3)

Step-by-step explanation:

9ay(2a-3)

hope it is helpful to you

Answer:

Step-by-step explanation:

a) Let's denote the number of coffees sold as 'x' and the number of cappuccinos sold as 'y'.

The equation that represents the given information is:

2.50x + 3.75y = 222.50

b) To solve the equation, we need to find the values of 'x' and 'y' that satisfy the equation.

Since we have two variables and only one equation, we cannot determine the exact values of 'x' and 'y' independently. However, we can find possible combinations that satisfy the equation.

Let's proceed by assuming values for one of the variables and solving for the other. For example, let's assume 'x' is 40 (number of coffees):

2.50(40) + 3.75y = 222.50

100 + 3.75y = 222.50

3.75y = 222.50 - 100

3.75y = 122.50

y = 122.50 / 3.75

y ≈ 32.67

In this case, assuming 40 coffees were sold, we get approximately 32.67 cappuccinos.

We can also assume different values for 'x' and solve for 'y' to find other possible combinations. However, keep in mind that the number of drinks sold should be a whole number since it cannot be fractional.

Therefore, one possible combination could be around 40 coffees and 33 cappuccinos sold.

The function g(x) in the form a(x-h)^2 + k is: \(g(x) = (x + 2)^2 - 4\)

Starting with\(f(x) = x^2\), the translation 2 units left and 4 units down would result in the following transformation:

g(x) = f(x + 2) - 4

Substituting\(f(x) = x^2:\)

\(g(x) = (x + 2)^2 - 4\)

Expanding the square:

\(g(x) = x^2 + 4x + 4 - 4\)

Simplifying:

\(g(x) = x^2 + 4x\)

Now we need to rewrite this expression in the form \(a(x-h)^2 + k.\) To do this, we will complete the square:

\(g(x) = x^2 + 4x\\g(x) = (x^2 + 4x + 4) - 4\\g(x) = (x + 2)^2 - 4\)

Therefore, the function g(x) in the form a(x-h)^2 + k is:

\(g(x) = (x + 2)^2 - 4\)

Where a = 1, h = -2, and k = -4.

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Answer:

<1=26

<2=154

<3=26

<4=26

<5=154

<6=154

<7=26

The interest amount is $622.85

The given parameters are:

The interest amount is calculated as:

I = P(1 + r/n)^(nt) - P

This gives

I = 1000 * (1 + 4.5%/1)^(1 * 11) - 1000

Evaluate the products and the quotient

I = 1000 * (1 + 0.045)^(11) - 1000

Evaluate the sum

I = 1000 * (1.045)^(11) - 1000

Solve

I = 622.85

Hence, the interest amount is $622.85

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The ratio of the area of the first figure to the area of the second figure is 4:1

From the question, we are to determine the ratio of the area of the first figure to the area of the second figure

The two figures are similar

From one of the theorems for similar polygons, we have that

If the scale factor of the sides of two similar polygons is m/n then the ratio of the areas is (m/n)²

Let the base length of the first figure be ,m = 14 mm

and the base length of the second figure be, n = 7 mm

∴ The ratio of their areas will be

\((\frac{14 \ mm}{7 \ mm})^{2}\)

\(= \frac{196 \ mm^{2} }{49\ mm^{2} }\)

\(=\frac{4}{1}\)

= 4:1

Hence, the ratio of the area of the first figure to the area of the second figure is 4:1

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Answer:

L.4118.36.

Step-by-step explanation:

Para determinar en cuánto se convertirán L.3000 en 4 años al 8% de interés compuesto anual capitalizable por trimestres se debe realizar el siguiente cálculo de interés compuesto:

3000 x (1 + 0.08 / 4)^4x4 = X

3000 x (1 + 0.02)^16 = X

3000 x 1.02^16 = X

3000 x 1.3727 = X

4118.357 = X

Por lo tanto, tras 4 años de inversión al 8% de interés compuesto anual capitalizable por trimestres, la inversión valdrá L.4118.36.

The solution to the given system of equation is (3, 3, 3)

Given the following system of equation expressed as:

2x-y+5z=16

X-6у +2z=-9

3x+4y- z=32

Multiply equation 2 by 2 to have:

2x-y+5z=16

2X-12у +4z=-18

Subtract

10y+z = 34 .........4

Similarly

3X-18у +6z=-27

3x+4y- z=32

Subtract

-22y+7z = -59 ........... 5

Equate 4 and 5

10y+z = 34 .........4 * 7

-22y+7z = -59 ........... 5 * 1

_______________________

70y+7z = 238

-22y+7z = -59

Subtract

92y = 297

y = 3

Recall that

10y+z = 34

10(3) + z = 34

z = 3

Since x - 6y +2z = -9

x-6(3)+2(3) = -9
x - 18 + 6 = -9
x = 3

Hence the solution to the given system of equation is (3, 3, 3)

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Answer:

153.94cm squared

Step-by-step explanation:

π×7×7

=153.93804

=153.94cm squared

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

Speed(Km/hr)___No of players__Relative freq

10--13.9_________4______4/612 = 0.0065359

14-17.9_________ 7______7/612 = 0.0114379

18-21.9________20_____20/612 = 0.0326797

22-25.9_______ 83_____83/612 = 0.1356209

26-29.9_______319____319/612 =0.5212418

30-33.9______ 179_____179/612 = 0.2924836

The percentage of players that had a top speed between 22 and 25.9 km/h was : 0.1356209 × 100 = 13.56%

c. The percentage of players that had a top speed less than 13.9 km/h was: 0.0065359 × 100 = 0.65%

Answer:

\(4 \times 39.37 = 157.48\)

Answer:

3.141592653589793

Step-by-step explanation:

Normally, you only need to memorize the digits up to 3.1415926. Of course, there are more digits of pi, but you don't need to know that much digits of pi.

Answer:

3.14159265359

Step-by-step explanation:

The distance between the start of the walkway and the middle person is 52 feet.

It is given that a 100 foot long moving walkway moves at a constant rate 6 feet per second.

AI steps into the start of the walkway and stands this means speed of AI is 6 feet per second.

Bob steps onto the start of  he walkway two second later and stolls forward along walkway 4 feet per second that means 10 feet [per seconds.  

And CY reaches the starts of the walkway and walks briskly forward beside the walkway at a rate of 8 feet per second.

At the time s we gave that,

\(\frac{8(s-4)+10(s-2)}{2}\) = 6s

\(\frac{8s -32 + 10s - 20}{2}\)  = 6s

      18s - 52 = 12s

              6s  = 52

                s  = \(\frac{26}{3}\)

At the time AI has travels,  

6* \(\frac{26}{3}\) = 52 feet.

Therefore distance between the start of the walkway and the middle person is 52 feet.

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Solution

For this case we can do this:

5/7 km

The reason is because we just need to divide the total distance (5km) by the 7 friends

The measure of the frame in feet of the length and width are 3.667 feet and 2.125 feet respectively.

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here: The measure of the frame is 8.5 inches and 11 inches

a) if the frame is 4 papers long then we  have the length of the frame as

11×4=44 inches (since he lays the paper along the edge of frame)

We know 1 inch= 0.0833 foot

Thus      44 inches= 3.66667 foot

b) Again if he lays the paper along the short edge than the width of the frame is 3×8.5=25.5 inches

∴25.5 inches= 2.125 feet

Hence, The measure of the frame in feet of the length and width are 3.667 feet and 2.125 feet respectively.

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Answer:

according to another user on Brainly the variable is n=-21

Step-by-step explanation:

subtract 986 from both sides first.why? Because that is that is going to isolate the variable.

hope this helps! :)

Answer:

Step-by-step explanation:

To write y as a function of x using the given functions, we can substitute the value of "a" in the first equation with the expression "-5x + 1" from the second equation.

Given:

y = -3a + 3

a = -5x + 1

Substituting the value of "a" in the first equation:

y = -3(-5x + 1) + 3

Now, let's simplify this expression:

y = 15x - 3 + 3

y = 15x

Therefore, y can be expressed as a function of x as:

y = 15x

For the relation to not to be a function we need the same value of x in (x,y) that gives off different values (y).

Now plugging in the value of k,

hence , the relation won't be function if k would be equal to 3

The value of k for which the relation R = {(2k+1, 3), (3k−2, −6)} is not a function is k = 3.

In general terms, a function is a mathematical rule or relationship that maps one set of values (the input or domain) to another set of values (the output or range). In other words, it's a specific process that takes some input and produces a corresponding output.

For the given relation R to be a function, each input in the domain should have exactly one corresponding output in the range.

We can determine whether the relation R is a function by checking if both ordered pairs have the same first coordinate. If they do, then the relation is not a function.

Let's equate the first coordinate of the ordered pairs:

2k+1 = 3k-2

Solving for k, we get:

k = 3

If we substitute k = 3 into the relation, we get:

R = {(2(3)+1, 3), (3(3)−2, −6)}

R = {(7, 3), (7, -6)}

Since both ordered pairs have the same first coordinate of 7, the relation R is not a function.

Therefore, the value of k for which the relation R = {(2k+1, 3), (3k−2, −6)} is not a function is k = 3.

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The number of inches apart that the four bolts will be along the circumference of the metal plate shown in the figure is 9.425 inches.

The circumference refers to the total distance around a circle.

The circumference can determined using the following formula.

Circumference = 2πr

Diameter of the circle = 12 inches

Radius = 12/2 inches = 6 inches

Circumference = 2 x 22/7 x 6

= 37.7 inches

The number of bolts along the circumference = 4

Distance between the four bolts = 9.425 inches (37.8 ÷ 4)

Thus, using division operation, the distance apart of the four bolts is 9.425 inches.

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Answer:

\((x-4)(x^2+6)\)

Step-by-step explanation:

x³-4x²+6x-24 is our equation

Once we factor it we get

\((x-4)(x^2+6)\)

Answer:

Step-by-step explanation:

B was wrong!!

Answer: A

Step-by-step explanation: Just got it right.

The period of the sound wave created by the tuba is approximately 0.0134 seconds.

The speed of sound in air is given as 343 meters per second. The formula relating the speed of sound, wavelength, and period of a wave is:

v = λ × f

Where:

v = speed of sound (343 m/s)

λ = wavelength (4.61 m)

f = frequency (unknown)

To find the period, we need to determine the frequency of the sound wave. The period (T) is the reciprocal of the frequency (f), so we can rewrite the formula as:

v = λ / T

Rearranging the equation to solve for the period (T), we get:

T = λ / v

Substituting the given values, we have:

T = 4.61 m / 343 m/s

Calculating the value, we find:

T ≈ 0.0134 seconds

Therefore, the period of the sound wave created by the tuba is approximately 0.0134 seconds.

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The roots of the given polynomial using the rational zero theorem are;  2, -4 and 6.

We are given the polynomial;

y = x³ - 4x² - 20x + 48

Since all coefficients are integers, we can apply the rational zeros theorem.

The trailing coefficient (the coefficient of the constant term) is 48

Find its factors (with the plus sign and the minus sign): ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, ±48.

These are the possible values for p.

The leading coefficient (the coefficient of the term with the highest degree) is 1.

These are the possible rational roots:

±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, ±48.

Checking the possible roots: if a is a root of the polynomial P(x), the remainder from the division of P(x) by x - a should equal 0 (according to the remainder theorem, this means that P(a)=0

Plugging in those values, the only ones that yield P(a) = 0 are; 2, -4 and 6.

Thus, these are the roots of the given polynomial.

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A circle having radius 5 and centre at (0,0) has equation x² + y² = 25.

What is the equation of circle?

A circle is a closed curve that extends outward from a set point known as the centre, with each point on the curve being equally spaced from the centre. A circle with a (h, k) centre and a radius of r has the equation:

(x-h)² + (y-k)² = r²

Let (x,y) be any point on the circle.

Given that centre of the circle is origin (0,0).

Now, we know that the distance from any point on the circle to the centre is equal to the radius of the circle.

So, distance between point (x,y) and centre (0,0)  is equal to radius of the circle which is given 5 units.

Now, using the distance formula -

√[(x - 0)² + (y - 0)²] = 5

Squaring on both the sides of the equation -

(x - 0)² + (y - 0)² = 25

So, the equation of the circle with radius 5, centred at the origin is x² + y² = 25.

Therefore, the equation is x² + y² = 25.

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