1. A rectangle has a length that is three feet more than twice its width.
(a) If the width of the rectangle is represented
by the variable w, give an expression for
the length of the rectangle in terms of w.
(b) What would the perimeter of this
rectangle be if the width was 10 feet?
(c) The perimeter of the rectangle is 78 feet. Set up an equation using w that models this
situation. Solve it and state the values for both the width and the length of the rectangle.

The weight of both books when put on the scale together is [tex]\frac{37}{24}=1\frac{13}{24}[/tex].

The smallest positive integer that is divisible by both a and b is known as the least common multiple (lcm), lowest common multiple (lcm), or smallest common multiple of two numbers a and b in mathematics and number theory.

Let the weight of the two books Paulette had be x and y.

The weight of one of the books is x = 7/8 pounds.

The weight of the other book is y = 2/3 pound.

If the books are put on the scale then the total weight of the books will be:

[tex]x+y=\frac{7}{8}+\frac{2}{3}[/tex]

The least common multiple or LCM of 8 and 3 is 24.

[tex]x+y=\frac{21+16}{24}[/tex]

[tex]x+y=\frac{37}{24}[/tex]

The correct option is (B) [tex]\frac{37}{24}=1\frac{13}{24}[/tex].

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Answer:167

Step-by-step explanation: 360 - 90-35-68=167

Answer:

i) -2.5

ii) 3/4 - 0.250

iii) 0.282

iv) 85% - 0.850

v) [tex]\sqrt{3\\[/tex] - 1.7320

Step-by-step explanation:

I will assume that DC is 16,

16 x 2= 32

Answer:

A) 0.

Step-by-step explanation:

There is no yellow on the plane, therefore, the probability that the spinner would land on a nonexistent part of the plane is 0.

Answer:

a=4+3b-c

a=5+6b-9c/ 3

a=9+9b-10c /4

The expression can use mental math to simplify the expression

9.15. 2 most easily is (15×2)×9.

Expression:

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression.

Possible expressions for the given question:

1) (15×9)×2

2)(15×2)×9

3)(2×9)×15

1⇒ Becomes complicated because of multiplication of 15 and 9

2⇒ Becomes easy because of (15×2) and then multiplication with  9

3⇒ Becomes complicated because of multiplication of 15 and (2×9)

Therefore,The expression can use mental math to simplify the expression 9.15. 2 most easily is (15×2)×9.

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3 times 15 will get us close to 45 tenths without going over

x=3

This is further explained below.

Generally, In the field of mathematics, a formula is referred to as an equation when it is used to represent the equivalence of two expressions by connecting them with the equals sign (=). In other terms, an equation is an expression that is used in mathematics.

In conclusion, The equation for the word problem is given as

x*15 ≡45

Therefore

x ≡45/15

x=3

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The magnitude of an earthquake is related to the relative intensity by

magnitude = log(relative intensity).

Magnitude is a measure of earthquake size and remains unchanged with distance from the earthquake. Intensity, however, describes the degree of shaking caused by an earthquake at a given place and decreases with distance from the earthquake epicentre.

A better measure of the size of an earthquake is the amount of energy released by the earthquake, which is related to the Richter Scale by the following equation:

Log E = 11.8 + 1.5 M

(where Log refers to the logarithm to the base 10, E is the energy released in ergs and M the Richter magnitude).

Magnitude is determined from measurements on seismographs. Intensity measures the strength of shaking produced by the earthquake at a certain location. Intensity is determined from effects on people, human structures, and the natural environment.

An earthquake's magnitude is inversely proportional to its relative intensity (magnitude = log) (relative intensity)

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Answer:

10 masks

Step-by-step explanation:

divide 6 1/4 yards by 5/8 yards

change 6 1/4 to an improper fraction - 25/4

25/4 ÷ 5/8

to divide fractions, find reciprocal of divisor

25/4 * 8/5

=10

so 10 masks

Answer:

$63

Step-by-step explanation:

Penny = $0,01

Nickel = $0.05

Dime = $0.1

Quarter= $0.25

Number of pennies = 6*50 = 300

Number of nickels = 5*40= 200

Number of dimes = 4*50= 200

Number of quarters = 3*40 = 120

The total amount of money:

300*0.01+ 200*0.05 + 200*0.1 + 120*0.25 = $63

Answer:

12

Step-by-step explanation:

___ * ___ * ___

At the first one you have 3 choices so

_3_ * ___ * ___

then you have two choices for the second and third code

so 3 * 2 * 2 = 12

The maximum value of the objective C = 5x -4y over given constraints is

In any optimization problem, when we need to either maximize or minimize some objective function for that we are given some limitations or logical conditions which the objective function  needs to satisfy in order to maximize or minimize.

These constraints are in the form of equalities or inequalities, where a feasible region satisfying all these equalities or inequalities is first found and then we maximize/minimize our objective on the boundary points of this feasible region.

Given problem is:

Maximize Objective function C = 5x-4y

When system of constraints are (i) x≥0 , (ii) y≥0 , (iii) 4 ≤y+ x

(iv) y ≤ (1/5)x +1

We will graph this system of constraints to find the feasible area.

x≥0,y≥0 represents that feasible area is in the 1st quadrant

For 4 ≤ x + y, we will use corresponding x+ y = 4 equality

When x= 0 then y=4 and when y=0 then x=4 , then y+ x = 4 is a line passing through (0,4) and (4,0)

When be substitute (0,0) in 4 ≤ x + y we get 4 ≤0 which is a false statement .

Therefore,4 ≤y + x is the region starting with line x+ y = 4 and area above this line in opposite direction of origin.

For y ≤ (1/5)x +1, we will use y = (1/5)x +1, put x= 0 we get y=1 and put y=0 then x= -5 , then y= (1/5)x +1 is a line passing through (0,1) and (-5,0)

And on substituting (0,0) in y ≤ (1/3)x +1 we get 0 ≤ 1 which is a true statement .

Therefore, y ≤ (1/5)x +1 is region including the line y = (1/5)x +1 and area on the side of this line that is towards origin

The feasible region is shown in the attached picture with the boundary points of the shaded area.

ABC is the shaded area is feasible area,  where A= (0,4)   ,B= (2.5, 1.5 ), C= (0,1)

Z at A : 5(0) -4 (4) =-16

Z at B : 5(2.5) -4(1.5) =6.5

Z at C : 5(0) -4(1) = -4

Clearly, maximum value of z in feasible area is Z= 6.5 at point (2.5, 1.5)

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Using translation concepts, the rule for each vertex of the triangle after the translation 9 units right and 9 units down is given by:

(x,y) -> (x + 9, y - 9).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For this problem, the transformations on the triangle are given as follows:

Thus the rule for each vertex of the triangle after the translation 9 units right and 9 units down is given by:

(x,y) -> (x + 9, y - 9).

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The value of the expression, 8 + (18 ÷6) x (2 x 9 - 4) is 50.

The order of operations gives a guideline with which mathematical operations are solved. The order of operations are provided using the BODMAS rule.

According to BODMAS, the order of operations are brackets, of, division, multiplication, addition and subtraction.

The expression is:

8 + (18 ÷6) x (2 x 9 - 4)

The terms in the bracket would be solved first :

(18 ÷6) = 3

(2 x 9 - 4)

The multiplication would be solved first, then 4 would be subtracted from the result of the multiplication : 18 - 4 = 14

The expression becomes: 8 + 3 x 14

The multiplication would be solved first and then 8 would be added to the result: 8 + 42 = 50

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Answer:

33

Step-by-step explanation:

43 - 10 = 33

Answer:33

Step-by-step explanation:hope it helps, brainliest? i could really use it

The whole number that represents the value of the underlined digit in each case is as follows:

The value of a digit is the worth of the digit within its number place.

The number place determines the value of an underlined digit.

For instance, the number place values of 5 in the first and second situations are in the thousands and ten thousand place values.

The number place value of 9 in the third situation is in the hundred thousand place values, while the place value of 5 in the last example is in the ten place value.

Thus, the value of an underlined digit depends on its place value, and the place value is a digit's value based on its position.

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For each number, give the whole number that represents the value of the underlined digit.

155,349

651,907

947,502

317,055

Answer:

1/4

Step-by-step explanation:

Convert fractions to decimals

[tex]1-0.25-1/2\\1-0.25-0.5\\[/tex]

Add/Subtract

[tex]1-0.25-0.5\\= 0.75-0.5\\= 0.25\\= \frac{1}{4}[/tex]

The sum of -9 + 6 on the number line will be calculated by starting from -9 and counting 6 times to the right. This will be -3.

It should be noted that a number line simply means the straight line which has numbers that are arranged at equal segments or intervals that are along its length in Mathematics. It should be noted that the number line is usually shown horizontally and that it can be extended in any direction.

It should further be noted that the number line simply gives a representation of the graduated straight line which can be used to represent real numbers visually. In this case, every point on the number line simply corresponds to the real number, and every real number simply corresponds to a point.

It should further be noted that counting the numbers to the right indicates addition while to the left indicates subtraction.

In conclusion, the sum of -9 + 6 on the number line will be calculated by starting from -9 and counting 6 times to the right and this gives -3.

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Mary's expected payback based on the information illustrated is 0.865. This isn't a fair game.

Based on the information, the chances of Donna winning will be 1/2.

It was also stated that each day Donna and Mary toss a coin to see who buys the other person coffee ($1.73 a cup).

Therefore, Mary's expected payback will be:

= (0 × 1/2) + (1.73 × 1/2)

= 0 + 0.865

= 0.865.

Therefore, Mary's expected payback based on the information illustrated is 0.865. This isn't a fair game.

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11/4 or 2.75 part is remaining out of 13 ¼

Total sheet of steel will be 13 ¼

So dividing the whole sheet into 3 parts : let one piece be x and other be y and the remaining be z

as per the question x=2 3/4 and y amounts to = 31/4

so we need to find z

x + y + z= 13 1/4 (equation 1)

substituting the value of x= 2 3/4 and y = 31/4 in equation 1

2 3/4 + 31/4 + z= 13 1/4

converting mixed fraction into improper fraction

11/4 + 31/4 + z =53/4

z =53/4 -(11/4 + 31/4)

z = 11/4

hence z= 11/4

Therefore, out of 13 ¼, 11/4 or 2.75 part remains

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Answer:

2

Step-by-step explanation:

PRT = I = 2700

P = 27,000

R = 0.05

Find T

2700 = 27000 x 0.05 x T

T = 2700/ ( 27000 × 0.05 ) = 2 years

Answer:

The third option.

The others are being multiplied by a negative, which a negative times a negative is a positive, but the third is 3 negatives and 1 positive so it is positive.

Step-by-step explanation:

Hope it helps! =D

Answer: 9/2

Step-by-step explanation:

Answer: [tex]j=1, k=2[/tex]

Step-by-step explanation:

[tex]4(x+j)+k(3x-5)=10x-6\\\\4x+4j+3kx-5k=10x-6\\\\x(4+3k)+(4j-5k)=10x-6\\\\\implies 4+3k=10 \implies k=2\\\\\implies 4j-5k=4j-10=-6 \implies j=1[/tex]

The equation  4x + 12 = -2x + 16 is one solution.

A statement of equality between two expressions consisting of variables and/or numbers.

Given:

4x + 12 = -2x + 16

Now solving for x

4x + 2x = 16 - 12

6x = 4

x= 4/6

x=2/3

Hence, the equation  4x + 12 = -2x + 16 has one solution.

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The value of (f + g)(x) can be find out by adding both given functions f(x) and g(x) and its value will be x² - x + 6.

What is function ?

A function is a relationship between inputs and outputs where each input has precisely one output and the output can be linked to its input.

The given functions are :

f(x) = x² + 1

g(x) = 5 - x

We now have to find the value of (f + g)(x).

We know that the value of (f + g)(x) can be calculated by simply adding the values of both given functions which are f(x) and g(x).

So ,

(f + g)(x) = f(x) + g(x)

Now , let's substitute the values of both functions f(x) and g(x) into the above equation , so we will get :

(f + g)(x) = (x² + 1 ) + (5 - x)

Rearranging and solving the terms we get the value of (f + g)(x) as :

(f + g)(x) = x² - x + 6

Therefore , the value of (f + g)(x) can be find out by adding both given functions f(x) and g(x) and its value will be x² - x + 6.

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to get the y-intercept, we can simply set x = 0 and solve for "y".

[tex]2x-4y=4\implies 2(\stackrel{x}{0})-4y=4\implies -4y=4\implies y=\cfrac{4}{-4}\implies y=-1 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (0~~,~~-1)~\hfill[/tex]

The value of the expression -1/2 * (10x - 4) - (4x - 2) is -9x + 4

The expression is given as

-1/2 (10x-4) -( 4x-2)

Rewrite properly as

-1/2 * (10x - 4) - (4x - 2)

Open the brackets

So, we have

-1/2 * (10x - 4) - (4x - 2) = -5x + 2 - 4x + 2

Collect the like terms in the above expression

So, we have

-1/2 * (10x - 4) - (4x - 2) = -5x  - 4x + 2 + 2

Evaluate the like terms in the above expression

So, we have

-1/2 * (10x - 4) - (4x - 2) = -9x + 4

Hence, the value of the expression -1/2 * (10x - 4) - (4x - 2) is -9x + 4

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