Find a value for y for which the expression (1-y)(3-y)(6-y) has each given value

i. -70

ii. 120

The Area of a Rectangle

A rectangle of width W and length L has an area calculated as:

We are given the side lengths W = 2/3 and L = 5/12. The order of the sides is not important because the area is a product and it's a commutative operation.

Calculating:

Multiplying numerators and denominators separately:

This fraction can be simplified but if we do, we won't be able to find the correct choice, thus:

Area = B: 10/36 square foot

Answer:

$26,986.29

Step-by-step explanation:

We can use the formula for calculating the depreciation of an asset over time:

wor

\(\bold{D = P(1 - \frac{r}{100} )^t}\)

where:

D= the current value of the asset

P = the initial purchase price of the asset

r = the annual depreciation rate as a decimal

t = the number of years the asset has been in use

In this case, we have:

P = $39,600

r = 12% = 0.12

t = 3 years

Substituting these values into the formula, we get:

\(D= 39,600(1 - \frac{12}{100})^3\\D= 39,600(1 - 0.12)^3\\D= 39,600*0.88^3\\D= 39,600*0.681472\\D=26986.2912\)

Therefore, the car is worth approximately $26,986.29 after 3 years of depreciation at a rate of 12% per annum.

Answer:

$26,986.29

Step-by-step explanation:

As the car's value depreciates at a constant rate of 12% per annum, we can use the exponential decay formula to create a function for the value of the car f(t) after t years.

\(\boxed{f(t)=a(1-r)^t}\)

where:

In this case, the initial value is $39,600, and the rate of depreciation is 12% per year. Therefore, the function that models the value of the car after t years is:

\(f(t)=39600(1-0.12)^t\)

\(f(t)=39600(0.88)^t\)

To calculate the value of the car after 3 years, substitute t = 3 into the function:

\(\begin{aligned} f(3)&=39600(0.88)^3\\&=39600(0.681472)\\&=26986.2912\\&=26986.29\;(\sf 2\;d.p.)\end{aligned}\)

Therefore, the car is worth $26,986.29 after 3 years.

Answer:

35 days

Step-by-step explanation:

First division the total money

with per hour earn

$420/$12

=35 hour's

35/24

=about 1 hour45 minutes

The given function f(x) is:

Let's start finding f(4) by replacing x=4:

Now, find f(4+h) by replacing x=4+h:

Thus:

The answer is option b. 3

9514 1404 393

Answer:

  3.2 +r

Step-by-step explanation:

When r is added to 3.2, the sum is ...

  3.2 +r . . . . . . million dogs entering shelters annually

_____

Additional comment

The question asked cannot be answered using the information given in the problem statement. Information is given as to numbers of animals entering shelters. The question asks for the number of animals in shelters. That answer depends on the number leaving, which is not given.

Answer: Height = 20 inches, Width = 36 inches

Step-by-step explanation:

Let the height be \(h\) and the width be \(h+16\).

Using the formula for the perimeter of a triangle,

\(2(h+h+16)=112\\\\2(2h+16)=112\\\\2h+16=56\\\\2h=40\\\\h=20 \implies h+16=36\)

Answer:

\(\displaystyle \frac{cd^6}{a^4b^2}\)

Step-by-step explanation:

\(\displaystyle \frac{a^{-4}b^{-2}cd^6}{e^{-7}}\\\\=a^{-4}b^{-2}cd^6e^7\\\\=\frac{cd^6}{a^4b^2}\)

Notice that the variables with negative exponent that were originally in the denominator went to the numerator (like with \(e^{-7}\)) and became positive, and vice versa with those originally in the numerator went in the denominator (like with \(a^{-4}b^{-2}\)) and also became positive.

Step-by-step explanation:

a‐⁴b‐²cd⁶

_______

e‐⁷

cd⁶e⁷

_____

a⁴b²

Answer:

200 lbs.

Step-by-step explanation:

Divide mass value by 16 to convert oz to lbs.

3,200/16=200

The correct image include the following: B. Green: image A.

In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

By applying a rotation of 270° clockwise about the point (1, 2) to the coordinate of the vertices of blue block D, the coordinate the vertices of of its image would be located at the position of the Green: image A.

In this context, we can reasonably infer and logically deduce that Green: image A is the correct transformed shape.

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The value of expression (s - f) (- 7) would be,

⇒ (s - f) (- 7)  = 119

We have to given that,

Functions are defined as,

⇒ s (x) = 2x²

⇒ f (x) = 3x

Now, We can find the value of (s - f) (- 7) is,

⇒ (s - f) (- 7)

⇒ s (- 7) - f (- 7)

⇒ 2 (- 7)² - (3 × - 7)

⇒ 2×49 + 21

⇒ 98 + 21

⇒ 119

Therefore, The value of expression (s - f) (- 7) would be,

⇒ (s - f) (- 7)  = 119

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Answer:

f(2) = 15

for f(x) = 4, x = 6

Step-by-step explanation:

f(2) means f(x) for x = 2.

in the table for x = 2 we see f(x) = 15.

the second question : f(x) = 4

so, where in the table do we find f(x) = 4 ? ah, for x = 6 do we find f(x) = 4.

The correct answers are A) 7cm, C) 9cm and D) 12cm

The process of changing a given quantity that is expressed in one unit of measurement to another unit of measurement that is equivalent in value is referred to as conversion of units.

If every 2 cm on a scale drawing is equal to 7 feet in real life, then we can use proportions to find out which lines on the drawing would be greater than 21 feet in real life.

Let x be the length of a line on the scale drawing in centimeters. Then, we can set up the following proportion:

⇒  \(\frac{2cm}{7 feet} = \frac{x cm }{yfeet}\)

where y is the length of the line in real life. Solving for y, we get:

⇒  \(y = \frac{7 feet} {2cm} *x\)  

⇒  \(y = 3.5 x feet\)

If we put x = 2cm (given) then, y = 7 feet

For y = 21 feet, the value of x = 6cm.

Therefore, any line on the scale drawing that is greater than 6cm in length corresponds to a length greater than 21 feet in real life.

So, the lines on the drawing that are greater than 21 feet in real life are:

A) 7cm, C) 9cm, D) 12cm

Therefore, the correct answers are A) 7cm, C) 9cm and D) 12cm

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Answer:

y=2x+5

Step-by-step explanation:

−8x+4y=20

Step 1: Add 8x to both sides.

−8x+4y+8x=20+8x

4y=8x+20

Step 2: Divide both sides by 4.

4y4=8x+204

y=2x+5

Answer:

y=2x+5

Step-by-step explanation:

Let's solve for y.

20=8x+4y

Step 1: Flip the equation.

8x+4y=20

Step 2: Add -8x to both sides.

8x+4y+−8x=20+−8x

4y=−8x+20

Step 3: Divide both sides by 4.

4y

4

=

−8x+20

4

y=−2x+5

\(\begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} ~\hspace{7em} \begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\)

\(\log(x)=2\hspace{5em}\log(y)=3\hspace{4em}\log(2)\approx 0.3\hspace{4em}\log(3)\approx 0.48 \\\\[-0.35em] ~\dotfill\\\\ \log\left(\sqrt[3]{x^4\cdot y^2} \right)\implies \log\left(\left( x^4\cdot y^2 \right)^{\frac{1}{3}} \right)\implies \cfrac{1}{3}\log(x^4 y^2) \\\\\\ \cfrac{1}{3}[\log(x^4)~~ + ~~\log(y^2)]\implies \cfrac{1}{3}[4\log(x)~~ + ~~2\log(y)]\implies \cfrac{1}{3}[4(2)~~ + ~~2(3)] \\\\\\ \cfrac{1}{3}[8~~ + ~~6]\implies {\Large \begin{array}{llll} \cfrac{14}{3} \end{array}}\)

B is not true, because in the graph when x=0 y=30, and when x=3 y is not equal to 28 (that would be true if she finishes 2 homework points every 3 minutes). the final answer will be B

a. The amount he deposited at first is $975

b. This is a case of exponential growth

c. the monthly interest rate is 0.3%

d. The account balance after 6 months and 12 months are

e. it will take 10months

Compound interest is the interest you earn on interest. The amount earned or paid is expressed as;

A = p( 1+r/100)^t

where p is the principal and t is the time

Relating the equation ; b = 975(1.003)^m

therefore;

1. The initial amount deposited = $ 975

2. The case is an exponential growth because the balance will be creasing with increase in number of month.

3. The monthly interest rate =

1.003 = 1+r/100

r/100 = 1-1.003

r /100 = 0.003

r = 0.3%

4. the balance after 6 months

975(1.003)^6

= 975 × 1.018

=$ 992.55

after 12 months

= 975(1.003)^12

= $1010.68

5. if b = $1000

1000 = 975(1.003)^m

(1.003)^m = 1000/975

(1.003)^m = 1.03

m = 10 months.

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Answer:

7√3 + 7π/6 ≈ 15.790

Step-by-step explanation:

First, find the intersection:

7 cos(2x) = 7 − 7 cos(2x)

14 cos(2x) = 7

cos(2x) = 1/2

2x = π/3

x = π/6

From the graph:

On 0 ≤ x ≤ π/6, 7 cos(2x) > 7 − 7 cos(2x).

On π/6 ≤ x ≤ π/2, 7 − 7 cos(2x) > 7 cos(2x).

So the integral is:

\(\int\limits^\frac{\pi}{6} _0 {[7cos(2x)-(7-7cos(2x))]} \, dx + \int\limits^\frac{\pi}{2} _\frac{\pi}{6} {[(7-7cos(2x))-7cos(2x)]} \, dx\)

\(\int\limits^\frac{\pi}{6} _0 {[7cos(2x)-7+7cos(2x))]} \, dx + \int\limits^\frac{\pi}{2} _\frac{\pi}{6} {[7-7cos(2x)-7cos(2x)]} \, dx\)

\(\int\limits^\frac{\pi}{6} _0 {[14cos(2x)-7]} \, dx + \int\limits^\frac{\pi}{2} _\frac{\pi}{6} {[7-14cos(2x)]} \, dx\)

\([7sin(2x)-7x]|^\frac{\pi}{6} _0 + [7x-7sin(2x)]|^\frac{\pi}{2} _\frac{\pi}{6}\)

\([7sin(\frac{\pi }{3} )-\frac{7\pi }{6} ] - [7sin(0)-0 ] + [\frac{7\pi }{2} -7sin(\pi )] - [\frac{7\pi }{6} -7sin(\frac{\pi }{3} )]\)

\(7sin(\frac{\pi }{3} )-\frac{7\pi }{6} + \frac{7\pi }{2} -7sin(\pi ) - \frac{7\pi }{6} +7sin(\frac{\pi }{3} )\)

\(14sin(\frac{\pi }{3} )-\frac{7\pi }{3} + \frac{7\pi }{2}\)

\(7\sqrt{3} + \frac{7\pi }{6}\)

Answer:

Quadrilateral: 20.5 units

Triangle: 8.6 units

Step-by-step explanation:

Quadrilateral:
We can use the following formula to find the perimeter of a quadrilateral.

Perimeter = AB + BC + CD + DA

where AB, BC, CD, and DA are the lengths of the four sides of the quadrilateral.

In your case, the coordinates of the vertices of the quadrilateral are A(-3,-1), B(-3,3), C(2,3), and D(4,-1).

Using the distance formula, we can find the lengths of the four sides of the quadrilateral as follows:

\(AB = \sqrt{(-3 - (-3))^2 + ((-1) - 3)^2} = \sqrt{16} = 4\)

\(BC = \sqrt{(-3 - 2)^2 + ((3) - 3)^2} = \sqrt{25}= 5\)

\(CD = \sqrt{(2 - 4)^2 + ((3) - (-1))^2} = \sqrt{4+16} = 2\sqrt{5}\)

\(DA = \sqrt{(4 - (-3))^2 + ((-1) - 1)^2} = \sqrt{49} =7\)

Therefore, the perimeter of the quadrilateral is:

Perimeter = AB + BC + CD + DA

= \(4+5+2\sqrt5+7=20.5\) units

Triangle

The perimeter of a triangle is the total length of all three sides of the triangle. To find the perimeter of a triangle, we can use the following formula:

Perimeter = AB + BC + CA

where AB, BC, and CA are the lengths of the three sides of the triangle.

In your case, the coordinates of the vertices of the triangle are

E(-4,1), F(-2,3), and G(-2,4). Using the distance formula, we can find the lengths of the three sides of the triangle as follows:

\(EF = \sqrt{(-4 - (-2))^2 + ((1) - (3))^2} = 2\sqrt{2}\)

\(FG = \sqrt{(-2 - (-2))^2 + ((3) - (4))^2} = 1\)

\(EG = \sqrt{(-4 - (-2))^2 + ((1) - (4))^2} = \sqrt{4 + 9} = \sqrt{13}\)

Therefore, the perimeter of the triangle is:

Perimeter = EF + FG + EG

= 4 + 1 + \(\sqrt{13}\)

=8.6 units

Therefore, the perimeter of the quadrilateral is 20.5 units and the perimeter of the triangle is 8.6 units

Answer:

1/36

Step-by-step explanation:

On the first throw, the probability of rolling any particular number, 1 through 6, is 1 out of 6. So the chance of rolling a 4 is 1/6.

On the second roll, your probability of rolling a 2 is 1/6.

The 'trick' is knwoing what to do with those two numbers.

Here's the rule: If events are dependent on one another, you multiply the probabilities.

Any time you see a scenario where X has to happen and then some other thing (X, Y, or whatever) has to happen, the events are dependent.

Probability of rolling a 4 and then rolling a 2 = 1/6 * 1/6 = 1/36

Hope this helps.

Answer: 4

This problem requires basic division. If the restaurant divided 4/5 kg of butter with 1/5 kg on each dish, you would need to compute 4/5 divided by 1/5.

4/5 ÷ 1/5

Using the "KFC" method, or Keep, Change, Flip, you would keep the first number (in this case, 4/5), change the division sign, and flip the fraction to 5/1, or 5. We now have this:

4/5 x 5

To compute this equation, you must multiply the numerators of both of the numbers together. In this case, you would compute (4x5)/5, resulting with 20/5, or 4.

You can check this answer by re-multiplying the numbers together. 1/5 kg of butter per dish, multiplied by the total amount of dishes, 4, you would result in the original 4/5 kg of butter.

Hope this helps!

Answer:

5

Step-by-step explanation:

The calculated values of the sum of interior angles of the shapes are 1080 degrees and 360 degrees

The formula of the sum of interior angles of a polygon is

Sum = (n − 2) * 180

For the octagon, we have

n = 8

This means that

Sum of angles = (8 − 2) * 180

Evaluate

Sum of angles = 1080

For the square, we have

n = 4

This means that

Sum of angles = (4 − 2) * 180

Evaluate

Sum of angles = 360

Hence, the sum of interior angles of the shapes are 1080 degrees and 360 degrees

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The multiplication 3/4×8/9 can be used to address the problem in response (B). which is the correct answer that would be an option (B).

In mathematics, Multiplication operations perform Multiplying values on either side of the operator.

For example 4×2 = 8

As per option (B),

Jada rode her bike for 3/4 mile. Sarah rode her bike 8/9 the distance that Jada rode her bike.

Sarah rides her bike = Sarah rode (8/9) of the (3/4) that Jada rode.

Sarah rides her bike = 3/4 × 8/9

Therefore, this problem can be solved by performing the above multiplication.

Hence, the correct answer would be an option (B).

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The following expression (-3/5)x-7-(-12)+(3/10)x can be written in the simplest form as -3/10x+5( three over 10 times x plus 5). So, option c is correct.

An expression or mathematical expression is a finite arrangement of symbols that are well-formed in line with context-dependent criteria. To help define the logical grammar and order of operations, mathematical symbols can be used to represent variables, operations, functions, brackets, punctuation, and grouping. A sentence qualifies as a mathematical expression if it comprises one or more mathematical operations, at least two numbers, or variables. Mathematicians have the ability to multiply, divide, add, and subtract. The following is the structure of an expression: Expression, number/variable, and mathematical operator.

(-3/5)x-7-(-12)+(3/10)x

-3/5x-7+12+3/10x

-6/10x-7+12+3/10x

-3/10x+5

Three over 10 times x plus 5

Therefore, the following expression (-3/5)x-7-(-12)+(3/10)x can be written in the simplest form as -3/10x+5( three over 10 times x plus 5).

Hence, option c is correct.

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The equation of the line in fully simplified slope-intercept form is y = x + 7.

We have,

From the graph,

The coordinates of the line are:

(0, 7), (-7, 0), and (-2, 5).

We can use any coordinates the line touches on the graph.

We will use,

(0, 7) and (-7, 0)

The equation can be written in the form y = mx + c

m = (0 - 7) / (-7 - 0)

m = -7/-7

m = 1 ______(1)

And,

(0, 7) = (x, y)

So,

y = mx + c ______(2)

7 = 1 x 0 + c

7 = c

c = 7 ______(3)

Now,

From (1), (2), and (3).

y = x + 7

Thus,

The equation of the line in fully simplified slope-intercept form is y = x + 7.

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