Solve each formula for the indicated variable. V = lwh , for w

Distance between the points D and E is [tex]5\sqrt{3}[/tex] and the mid point of the line segment joining D and E is (1/2,5/2,7/2) .

Distance Formula is used to calculate distance between two given points.

the distance between points A(a,b,c) and B(x,y,z) is given by [tex]\sqrt{(x-a)^{2}+(y-b)^{2}+(z-c)^{2} }[/tex]

Mid point formula the mid point M(m₁,m₂,m₃) between the points  A(a,b,c) and B(x,y,z) is given by M(m₁=[tex]\frac{a+x}{2}[/tex],m₂=[tex]\frac{b+y}{2}[/tex],m₃=[tex]\frac{c+z}{2}[/tex])

To calculate the distance between the points D(0,0,0) and E(1,5,7) we will use distance formula.

Substituting the values in Distance formula we get

d=[tex]\sqrt{(1-0)^{2}+(5-0)^{2}+(7-0)^{2} }[/tex]

=[tex]\sqrt{1^{2} +5^{2} +7^{2} }[/tex]

=[tex]\sqrt{1+25+49}[/tex]

=[tex]=\sqrt{75} \\ 5\sqrt{3}[/tex]

to determine the midpoint M we will use mid point formula.

Substituting the values of the given points in the mid point formula we get

mid point = [tex](\frac{0+1}{2} ,\frac{0+5}{2} ,\frac{0+7}{2} )[/tex]=(1/2,5/2,7/2)

Therefore , Distance between the points D and E is [tex]5\sqrt{3}[/tex] and the mid point of the line segment joining D and E is (1/2,5/2,7/2) .

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Answer:

7x - 35

Step-by-step explanation:

This states the product of (5 less than x) and (7). Five less than x can be written as (x - 5), and 7 is just 7. The product of (x-5) and 7 is 7x - 35.

Hope this helped :)

Answer:

15 1/4 inches

Step-by-step explanation:

Length of the other piece

= 23 1/2 - 8 1/4

= 47/2 - 33/4

= 94/4 - 33/4

= 61/4

= 15 1/4 inches.

Answer: A number is divisible by 3 if the sum of the digits is divisible by 3. 

If the last two digits of a number are divisible by 4, the whole number is. For example, in 1,012, 12 is divisible by 4.

A large number is divisible by 8 if the last three digits are also divisible by 8 or are 000.

The function value at the minimum is -9

The function is given as:

f(x) = x^2 - 6x

Differentiate the function

So, we have

f'(x) = 2x - 6

Set the function to 0

So, we have

2x - 6 = 0

This gives

2x = 6

Divide by 2

x = 3

Substitute x = 3 in f(x) = x^2 - 6x

f(3) = 3^2 - 6(3)

Evaluate

f(3) = -9

Hence, the function value at the minimum is -9

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Answer:

f. 4+3=7

g. 23+8+4=35

h. 53+3+28=84

i. 11+17+92=120

j. 24+8+3=35

Step-by-step explanation:

Answer:

F = 4 + 4 = 8

G = 23 + 8 + 4 = 35

H = 53 + 3 + 27 = 83

I = 11 + 17 + 93 = 121

J = 24 + 8 + 3 = 35

Step-by-step explanation:

Answer:

√180 > 102/8

Step-by-step explanation:

√180 = 13.416407865
102/8 = 12.75

Answer:

Yes

Step-by-step explanation:

Because 180 is greater than 102

_____

8

Given set of numbers 13, 15, 16 represent an acute triangle.

By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.

Since the sum of the lengths of any two sides is greater than that of the third side, the set of numbers are the measures of a triangle.

Now we find the type of triangle.

We find the sum of the squares of the two smaller sides, and compare the sum to the square of the largest side.

The sum of the squares of the two smaller sides is,

= 13² + 15²

= 169 + 225

= 394

And 16² = 256

Since the sum of the squares of the two smaller sides is greater than the square of the largest side, the triangle must be an acute triangle.

Therefore, given set of numbers 13, 15, 16 represents an acute triangle.

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1. The coefficients of the factored polynomial x² - 8x + 15  are

2. The coefficients of the  factored polynomial 2x³ - 8x² + 24x are

3. The coefficients of the  factored polynomial 6x² + 14x + 4 are

Sincw we want to factor the polynomial x² - 8x + 15 in the form (ax + b)(cx + d), we have that

x² - 8x + 15 = x² - 3x - 5x + 15

= x(x - 3) - 5(x - 3)

= (x - 5)(x - 3)

comparing  (x - 5)(x - 3) with (ax + b)(cx + d), we see that the coefficients of the polynomial are

Sincw we want to factor the polynomial 2x³ - 8x² + 24x in the form 2x(ax + b)(cx + d), we have that

2x³ - 8x² - 24x = 2x(x² - 4x - 12)

Factorizing the expression inthe bracket, we have

= 2x(x² - 2x + 6x - 12)

= 2x[x(x - 2) + 6(x - 2)

= 2x(x - 2)(x + 6)

comparing  2x(x - 2)(x + 6) with 2x(ax + b)(cx + d), we see that  the coefficients of the polynomial are

Sincw we want to factor the polynomial 6x² + 14x + 4 in the form (ax + b)(cx + d), we have that

6x² + 14x + 4 = 6x² + 2x + 12x + 4

= 2x(3x + 1) - 4(3x + 1)

= (2x - 4)(3x + 1)

comparing  (2x - 4)(3x + 1) with (ax + b)(cx + d), we see that  the coefficients of the polynomial are

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The given sequence is geometric, with common ratio = 1.5

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Given: 10, 15, 22.5, 33.75,....

Here, 15/10 = 22.5/15 = 33.75/22.5 = 1.5

Since the given sequence follows the required condition for a sequence to be geometric, it is the one.

Hence, The given sequence is geometric, with common ratio = 1.5

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Using proportions, it is found that the deducted amounts each year are given as follows:

The tax rates are missing, and they are given as follows:

A proportion is a fraction of a total amount, and the measures can be related using a rule of three, which derives from proportional relationships.

Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures, involving operations such as division and multiplication, as they involve unit rates.

Considering that a year has 52 weeks, her yearly salary is given as follows:

52 x 570 = $29,640.

Considering the tax rate, the deducted amount for Social Security is given by:

0.0620 x 29640 = $1,837.68.

Considering the tax rate, the deducted amount for Medicare is given by:

0.0145 x 29640 = $429.78.

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Explanation:

x = length of the red and purple lunch box

y = length of the blue lunch box

volume = length*width*height

The volume expression for the red and purple lunch box is x*7.5*4 = 30x

Set this equal to the stated volume 300 cubic inches, and solve for x.

30x = 300

x = 300/30

x = 10

The red and purple lunch box has length of 10 inches.

-----------------

The blue lunch box has volume of

length*width*height = y*8*3 = 24y

Set this equal to 300 and solve for y

24y = 300

y = 300/24

y = 12.5

The blue lunch box has length of 12.5 inches

Therefore the blue lunch box is longer and is longer by 12.5-10 = 2.5 inches.

x= 6, y = 3 are the domain and range were interchanged, would the relation be a function.

What is domain ?

If the terms in range and domain were interchanged, one term 6 of domain relates with two different values of range,

x = 6, y = 2.5

x= 6, y = 3

  Since, a term of domain can't have two different values in range,

Therefore, interchanged relation will not be a function.

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Answer:

(0, -54)

Step-by-step explanation:

The y-intercept is when x=0.

[tex]y=-(2/3)(0-9)^2 \\ \\ =-(2/3)(81) \\ \\ =-54[/tex]

The slope of the line passing through the pair of points, (0 , 0) and (5 , -3), is -3/5.

The slope, m, determines the steepness of a line. It can be measured by the vertical distance from one point to another divided by the horizontal distance of the same points. The formula for solving the slope is:

m = (y2 - y1)/(x2 - x1)

where m is the slope

x1 and y1 are the coordinates of one point

x2 and y2 are the coordinates of the 2nd point

Given two points in the line, (0 , 0) and (5 , -3), plug in the values to the formula for the slope.

m = (y2 - y1)/(x2 - x1)

m = (-3 - 0)/(5 - 0)

m = -3/5

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As the value of Square root √75 is equals to 8.66, and the number 9 is larger than the number 8.66.

The value of Square root √75 is equals to 8.66, and the number 9 is larger than the number 8.66.

So, √75 <  9

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an=a1+d(n−1)  is the explicit and a recursive formula for each sequence .

See the pattern

1/8-0 =1/8

1/4-1/8 = 1/8

3/8-1/4 = 1/8

the explicit and a recursive formula for each sequence is an=a1+d(n−1).

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.

Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.

An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.

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Answer:

9 degrees

Step-by-step explanation:

If y varies directly with x , and y-15 when x-3, y is 60 when x is equal to 12.

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

y = kx            (Where k is the constant)

Here, we have given

15 = k3

k = 15/3

  = 5

So, y = 5x

When x = 12,

y = 5(12)

  = 60

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Correct question

Suppose y varies directly with x, and y = 15 when x = 3. What is y when x = 12?

Answer:

When she came to work the next day, she was delighted because four hundred sixteen hundred, nine hundred forty-three containers had been delivered. How many things (Problem 3) would fill them all?

https://www.louisianabelieves.com/docs/default-source/assessment/grade-7-answer-key.pdf

Step-by-step explanation:

[tex]f(x)=x^2-3x+20\\\\f(5)=(5)^2-3(5)+20\\\\f(5) = 25-15+20\\\\f(5)=\boxed{30}[/tex]

The eighth term of the given sequence 1/2, 1/4, 1/8, 1/16, 1/32 will be 1/256.

According to the give question.

We have a sequence 1/2, 1/4, 1/8, 1/6, 1/32

Since, the first term of the given sequence is 1/2.

The second term of the given sequence is 1/4.

The third term of the given sequence is 1/8.

Here, we can see that the numerator of each term is same i.e. 1. But the denominator is changing by power or 2. For the first term it is 2^1, for the second term it is 2^2, for the third term it is 2^3 and so on.

Therefore, the gneral formula for finding the nth term of the given sequence is given by

[tex]T_{n} = \frac{1}{2^{n} }[/tex]

So, the eighth term of the given sequence is 1/2^8 = 1/256.

Hence, the eighth term of the given sequence 1/2, 1/4, 1/8, 1/16, 1/32 will be 1/256.

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the two lines have the same slope and different y-intercept, which means that the lines are parallel.

Two linear equations:

y = a*x + b

y = c*x + d

Are parallel only if both have the same slope, which means that c = d, and the y-intercepts are different.

And are perpendicular if the slope of one of the lines is equal to the opposite of the inverse of the other slope, so:

a = -1/c

Now, our linear equations are:

3x + 2y = 6

y = (-3/2)*x + 5

We can write both of these in the slope intercept form:

3x + 2y = 6

2y = 6 - 3x

y = (6 - 3x)/2 = 3 - (3/2)*x

y = -(3/2)*x + 3

So the two lines have the same slope and different y-intercept, which means that the lines are parallel.

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After 6 weeks of training, Jorge will have run the equivalent of 13.5 races.

When two quantities, expressions, or numbers have the same value, they are said to be equal. An equivalent quantity can be expressed in a variety of ways, such as by a bar or an equivalent symbol. Because they can relate to it in their everyday lives, children find this topic to be particularly engaging for a variety of reasons.

A common or logical equivalency between several values or quantities can also be referred to as the equivalent. Equivalence is comparable to equality but distinct from it.

1 race = 20 miles

Lets assume he doesn't runs on Sunday and Thursday, thus

Miles he runs a week = (Monday + Tuesday + Friday) + ( Wednesday +Saturday)

1 week = (7 + 7 + 7) + (12 + 12)

           = 45 miles

If he runs for 6 weeks then

6 week's run = 6 × 45

                      = 270 miles

If 1 race is of 20 miles then in 6 weeks he would have ran  

= 270/20

= 13.5 races

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Answer:

10 3/4 lb

Step-by-step explanation:

she releases the 1 3/4 lb fish and keeps the 5 1/4lb, 3 1/2lb, and 2lb

The total weight of these three fish are

5 1/4lb

+

3 1/2lb

+

2lb

which equals 10 3/4lb

Based on the interest rates available to Michael, the option that would allow him to pay the least interest is B. 18-month loan with a 3.50% annual simple interest rate

The interest on the first option is:
= (7.25% x 12,000) x 12/12months in year

= $870

Interest on second loan:

= (3.5% x 12,000) x 18 / 12 months in year

= $630

Interest on third loan:

= (3.75% x 12,000) x 24/12 months in year

= $900

Interest on fourth loan:

= (2.75% x 12,000) x 36/12  months in year

= $990

In conclusion, the 18-month loan with a 3.50% annual simple interest rate gives the lowest rate.

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The volume of the cone as shown in the diagram is 192 cm²

Diameter in the question is given as 16cm

We need to find the radius of the cone to find the volume of cone which is half of the diameter = 16/2 = 8 cm

The height of the cone as given in the question is 3cm

The volume of the cone =1/3  (πr²h)

We are told to use the value of pi as 3 so we are not using 3.14 or 22/7 as the value of pie

Volume = 1/3  ( 3 × 8² × 3)

= 1/3  ( 9× 64)

  = 1/3  (576)

         = 192 cm²

Hence, the volume of the cone as shown in the diagram is 192 cm²

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The total change in the stock market from the beginning of the day to the end of the day is 89.75 points.

Here, we are given that the stock market goes down 30 1/2 points at the beginning of the day.

30 1/2 can be written as-

{(30*2) + 1}/2 = 61/2

Further it is given that the stock market goes up by 120 1/4 points at the end of the day.

120 1/4 can be written as-

{(120*4) + 1}/4 = 481/4

Thus, the total change in the stock market will be-

481/4 - 61/2

= 481/4 - 122/4

= 359/4

or 89.75

Thus, the total change in the stock market from the beginning of the day to the end of the day is 89.75 points.

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The two events are mutually exclusive if they cannot occur at the same time. A triangle is equiangular if it is equilateral. Never can one preclude the other. The two events are mutually exclusive if they cannot occur at the same time.

What pairs of occurrences can never coexist?

What are some examples of mutually exclusive events?

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