A garden table and a bench cost $783 combined. The garden table costs $83 more than the bench. What is the cost of the bench?

Answer:

946 gal

629 gal

Step-by-step explanation:

volume that evaporates = LWH

volume = (5.0 m × 100 cm/m × inch / 2.54 cm) × (12.0 m × 100 cm/m × inch / 2.54 cm) × 2.35 inch

volume = 218,550 in.³

volume = 218,550 in.³ × 1 gal / 231 in.³

volume = 946 gallons

You must add 946 gallons.

The loss to evaporation is 2.35 in.

The amount of rain is 20 mm

The net loss is

2.35 in. × 25.4 mm / inch - 20 mm = 39.69 mm

39.69 mm × 1 inch / 25.4 mm = 1.563 in.

The net loss now is 1.563 in. instead of 2.35 in.

We find the fraction of the the previous loss is the loss with rain and multiply by the previous loss.

1.563/2.35 × 946 gal = 629 gal

With rain, then 629 gallons of water must be added.

The coordinates of the point on the directed line segment is (-2, 4)

The points are given as

(-5, 8) and (-1, -8)

The ratio is given as

m : n = 3 : 1

The coordinates of the point are calculated as

Point = 1/(m + n) * (mx2 + nx1, my2 + ny1)

So, we have

Point = 1/(3+ 1) * (3 * -1 + 1 * -5, 3 * -8 + 1 * 8)

Evaluate

Point = 1/4 * (-8, 16)

So, we have

Point = (-2, 4)

Hence, the coordinates of the point on the directed line segment is (-2, 4)

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Answer:

5 hours and 48 minutes

Step-by-step explanation:

The equation for finding average speed is:  [tex]\frac{\text{Total Distance}}{\text{Total Time}}[/tex]

Let x represent the distance for both the journey from Riley's college to home and back. We can use one variable to represent this because both distances are the same.

We also know that the total round trip took 12 hours. Let y represent the time it took for Riley to drive from college to home. Therefore the time it takes for Riley to drive from home to college is 12 - y.

Using this information, we can set up a system of equations.

[tex]65.1=\frac{x}{y}\\\\69.6=\frac{x}{12-y}[/tex]

Multiply both sides of the first equation by "y" and both sides of the second equation by "12 - y".

[tex]65.1y=x\\\\835.2-69.6y=x[/tex]

Since both 65.1y and 835.2-69.6y are equivalent to x, we can set them equal to each other.

[tex]65.1y=835.2-69.6y[/tex]

Now, we have to solve the equation for time or "y".

[tex]65.1y=835.2-69.6y[/tex]

Add 69.6y to both sides

[tex]65.1y+69.6y=835.2[/tex]

[tex]134.7y=835.2[/tex]

Divide both sides by 134.7

[tex]y\approx6.2 $ hours = Six hours Twelve Minutes[/tex]

This is the time it took for Riley to drive from college to home, therefore the time it took for Riley to drive from home back to college is:

[tex]12-6.2=5.8=5$ hours and 48 minutes[/tex]

5 hours and 48 minutes

The solution to the expression (2.8 × 10⁻⁹) − (6.9 × 10⁻⁸) gives -6.62 * 10⁻⁸

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

Given the equation:

(2.8 × 10⁻⁹) − (6.9 × 10⁻⁸)

Making the exponents to be similar gives:

(2.8 × 10⁻⁹) − (69 × 10⁻⁹)

Simplifying gives:

-6.62 * 10⁻⁸

The solution to the expression (2.8 × 10⁻⁹) − (6.9 × 10⁻⁸) gives -6.62 * 10⁻⁸

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The speed of the faster cyclist is 30 mph.

Two cyclists, distance = 90 miles.

let the speed of one cyclist is = x and

let the speed of the other cyclist = 2x

time after which both the cyclists will meet = 3 hours.

Since they are travelling towards each other the effective speed = 2x ₊ x

= 3x

we know that time = distance/speed

3 = 90/3x

3x = 30

x = 10 mph speed of one cyclist.

speed of the other cyclist will be 3x = 3 × 10 = 30 mph

The speed of the fastest cyclist is 30 mph.

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Answer: H=2A/B

H=12 cm

Step-by-step explanation:

A = 1/2BH

2A=BH

H=2A/B

H=2(90)/15

H=180/15

H=12 cm

The height of the triangle is 12 cm.

To solve the formula A = (1/2)BH for H, we need to isolate the variable H.

A = (1/2)BH

Multiply both sides of the equation by 2 to eliminate the fraction:

2A = BH

To solve for H, divide both sides of the equation by B:

H = 2A / B

Now we have the formula for H in terms of A and B.

To find the height of a triangle with an area of 90 cm² and a base of 15 cm, we can substitute these values into the formula:

H = 2(90) / 15

H = 180 / 15

H = 12 cm

Therefore, the height of the triangle is 12 cm.

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Answer:

32

Step-by-step explanation:

The given set has 5 elements, meaning it has 2⁵ = 32 subsets.

This means the cardinality of the desired set is 32.

Answer:

the answer is 435

Step-by-step explanation:

the change between each line is 105, so we start to add and then you get the resul

The value of A in the number line is the in-between of 225 and 645 so it is 435.

In mathematics, a number line is a straight line containing numbers arranged at equal segments or periods throughout its duration.

In another word, a number line is basically a line in which infinite numbers have been written in ascending order or increasing order.

A horizontal number line is the most common representation and can be extended infinitely in any direction.

Given the number line,

Now if we count the interval of A between 225 and 645 it is 2(same).

So A must be between 225 and 645.

So,

225 - A = A - 645

2A = 870

A = 435

Hence "The value of A in the number line is the in-between of 225 and 645 so it is 435".

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We get that Shannon did not mix the correct shade as the ratios are not equal.

We are given that a particular shade of paint is made by mixing five parts of red paint with seven parts of blue paint.

This means that the ratio of the paints in that shade is

Red : Blue = 5 : 7.

Now, we are also given that to make the correct shade, Shannon makes 12 quarts of blue paint with 8 quarts of red paint.

Here the ratio becomes:

Red : Blue = 8 : 12

= 4 : 6

= 2 : 3

Now, since both the ratios are not equal, he did not mix the correct shade.

Therefore, we get that Shannon did not mix the correct shade as the ratios are not equal.

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The statement that best interprets the quotient is "there are 6( 1/4 ) two  - third in 4( 1/6 )".

In mathematics, the sum obtained by diluting two numbers is known as a quotient. The term "quotient" is used frequently in mathematics and is sometimes known as the integer portion of a division, a fraction, or a ratio.

Any integer may be used as the larger number in a fraction, which is a number that represents a percentage of the larger number. It is shaped like a denominator and a numerator.

For step 1:

The shaded part is:

4 + 1/6 = 4(1/6) = 25/6

Now, dividing the shaded part by the unshaded part,

( 25/6 ) / ( 2/3 ) = ( 25/6 ) × ( 3/2 )

( 25/6 ) / ( 2/3 ) = 25/4

( 25/6 ) / ( 2/3 ) = 6( 1/4 )

Hence, there are 6( 1/4 ) two  - third in 4( 1/6 ).

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The ordered pair which is a solution to every linear equation of the form given is; (0, 0).

It follows from the task content that the ordered pair which satisfies the equation of the form y =Mx be determined.

On this note, since the product of any real number, slope in this scenario and 0 is; 0.

Ultimately, it follows that the required ordered pair is; (0, 0) for any real number value of the slope, m.

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Answer:

  A.  A(l) = l² -6l

Step-by-step explanation:

You want a quadratic function for the area of a rectangle whose width is 6 feet less than its length.

Let l (ell) represent the length of the rectangle in feet. Then the width will be 6 feet less, or (l -6). The area is the product of length and width:

  A = LW

  A(l) = l(l -6)

  A(l) = l² -6l . . . . . . use the distributive property to eliminate parentheses

Answer:

Step-by-step explanation:

Answer:

19 cm.

Step-by-step explanation:

Area = h(a + b)/2

where h = height, and a and b are parallel sides,

145 = 10(10 + b)/2

290 = 100 + 10b

10b = 190

b  = 19 cm.

The cyclist cover 200 kilometer in 5 hours and his speed in miles are  25 miles per hour.

According to the statement

We have to find that the speed of the cyclist.

So, For this purpose, we know that the

Speed is the time rate at which an object is moving along a path

From the given information:

A cyclist his bike at a speed of 40 kilometers per hour

Then

The distance he covered in 5 hours = 40*5

The distance he covered in 5 hours = 200.

And then

The speed in miles :

We have given that the  1 mile is equal to 1.6 kilometers

Then

If he covers a 40 kilometers in a hour then

in miles it becomes = 40/1.6

In other words,

Speed in miles = 40/1.6

Speed in miles = 25 miles per hour.

So, The cyclist cover 200 kilometer in 5 hours and his speed in miles are  25 miles per hour.

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The value of the function f(-4) = 16.

A function is categorized as a relationship between a set of inputs that each have one output.

For the given function in the question;

f(x) = x ² , if  x < 0.

f(x) = 0 , if  x = 0.

f(x) = 2x + 1 , if  x > 0

Now, estimate the values;

(a) f(-4)

As, the value of the x to be substitute is negative, the function used will be.

f(x) = x ² ,for  x < 0.

Put the value x = -4

f(-4) = (-4)²

f(-4) = 16

The value of f(-4) = 16.

(b) f(0)

As the value of function is zero.

Then,

f(x) = 0 , if  x = 0.

Put x = 0 in function we will get.

f(x) = 0.

(c) f(2)

As the value to be substituted is positive, the function used is;

f(x) = 2x + 1 , if  x > 0

Put x = 2

f(2) = 4 + 1

f(2) = 5

Thus, the value of f(2) is 5.

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The image would also have two pairs of parallel sides

The given parameters are:

The translation transformation is a rigid transformation

This means that, it keeps the orientation that is being transformed

The initial figure has two pairs of parallel sides

Hence, the image would also have two pairs of parallel sides

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Start by dividing both sides by G, giving us

[tex]\frac{F}{G}=\frac{m_{1} m_{2} }{d^{2} } }[/tex]. Multiply both sides by d^2. [tex]\frac{F}{G}(d^{2})=m_{1} m_{2}[/tex].

Finally, divide both sides by m2.

[tex](\frac{F}{G}\div{m_{2}}) (\frac{d^{2} }{m_{2} } )=m_{1}[/tex]

Hope this helps! This was a tough problem for me too.

To address the issue, we must understand what the converse of a statement implies. The statement's opposite is true if a=bc and a/b=c.

By switching the condition and the result, a conditional statement can be made into its opposite. The converse of a statement is q—->p if the statement is p—->q. In the provided question, the condition is stated as a/b=c, and the answer is a=bc if the condition holds.

We must create the result, the condition, and the condition will be the new result in order to discover the opposite of this assertion. As a result, a=bc will be the condition for converse, and a/b=c will be the outcome if the condition is satisfied.

As a result, if a=bc then a/b=c., the supplied sentence has the opposite meaning.

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The square root of one hundred forty is less than one hundred five ninths. So, option D is correct.

According to this question we have to compare the square roots of both numbers One Hundred Forty and One Hundred Five Ninths. So, we have to calculate their square roots.

The square root of One hundred Forty: √140

The square root of One hundred Forty:  11.832

The square root of One Hundred Five Ninths: √159

The square root of One Hundred Five Ninths: 12.609

Comparing both of their square roots we can clearly see that :

           (11.832) < (12.609)

The square root of 140 < Square root of 159

Hence, option D is correct. The square root of 140 is less than 159.

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Answer:

the scientific approach led to the birth of modern psychology in the 1800's as psychologists argued that ideas about human behavior and mental processes should be supported by this. In the 1800's, psychologists established these for the (scientific study of human behavior and mental processes).

Step-by-step explanation:

Answer:

x = (- [tex]\frac{13}{2}[/tex], 0)
y = (0,26)

Step-by-step explanation:

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

Answer:

True

Step-by-step explanation:

We use definitions to help us in this problem. The definition of an integer is a whole number that is not a fraction or has any fractional value. This definition includes all whole numbers, so we know that all whole numbers can be classified as integers. That's one condition done. The definition of a rational number is a number that can be written as a fraction. All whole numbers can be written as a fraction (i.e. 12/1, -3/1, 10000/1). This means that all whole numbers are also rational numbers, giving us our final answer of True.

FINAL ANSWER: True

Answer:

Width = 15 ft

Step-by-step explanation:

Given formula,

→ A = L × W

Let us assume that,

→ Length = 4x

→ Width = x

→ Area = 900 ft²

Then the value of width will be,

→ A = L × W

→ 900 = 4x × x

→ 4x² = 900

→ x² = 900/4

→ x = √225

→ [ x = 15 ft ]

Hence, the value of width is 15 ft.

The polynomial function is V(x) = x^3 - 7x^2 + 10x and domain of x is (5,6]

Here we are given that the length of the box is x

Also, the width of the box should be 5 feet shorter than the length

Thus, width = x - 5

and the height should be 3 feet longer than the width

Thus, height = x - 5 + 3

= x - 2

Now the volume of the box = length × width × height

Volume = x (x-5) (x-2)

V(x) = (x^2 - 5x) (x-2)

V(x) = x^3 - 2x^2 - 5x^2 + 10x

V(x) = x^3 - 7x^2 + 10x

Now, looking at the options, we see that option C is eliminated.

Now, let us look at the domain of x

Since width cannot be negative (x-5) > 0

⇒ x > 5

Now in option A domain is (0, 6], but x cannot take values from (0,5). Thus, option A is eliminated.

Similarly, we can eliminate option B also since x cannot take values from (0, 2)

Thus, option 4 is the correct answer.

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Your question was incomplete. Check for the missing options below, in the figure attached.

We can use the concept of unitary method to solve the question.The weight of 6 cubic feet of water is 0.19 Ton.

Unitary method helps us in finding the solution to seemingly complicated problems, here we have been given the amount of water that one cubic foot can hold, first we need to find out how much water 6 cubic feet can hold.

1 cubic foot hols 7.48 gallons of water

6 cubic feet holds 7.48x6 gallons of water=44.88 gallons

Next we know how much 1 gallon of water weighs in pounds,we need to find out how much 44.88 gallons of water weigh in pounds first and then convert it to tons.

1 gallon weighs 8.33 pounds

44.88 gallons weighs 8.33x44.88=373.8504 pounds

1 Ton=2000 pounds

373.8504 pounds=[tex]\frac{373.8504}{2000}[/tex]=0.1869 Ton≈0.19 Ton

Thus we can see that 6 cubic feet of water weighs 0.19 Ton, we used unitary method step by step to reach this result.

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Answer:

13+2n

Step-by-step explanation:

'two times a number' means 2n

'13 more' means we add 13 to this, so 13+2n is the answer.

Answer:

2.204×[tex]10^{9}[/tex]

Step-by-step explanation:

Convert to scientific notation.