60 can be expressed as the sum of 5 consecutive numbers as follows:

60 = 10 + 11 + 12 + 13 + 14

The sum of the greatest and the smallest of these 5 consecutive numbers is 24.

90 can also be expressed as the sum of 5 consecutive numbers. What is the sum of the greatest and the smallest number of these 5 consecutive numbers?









A 36 B 46

C 54 D 84









please someone answer

Answer: The length is 10ft, the width is 7ft.

Step-by-step explanation:

Let L be the length

Let w be the width

The equation for the perimeter is:

2L+2w=34

We also know that L=2w-4

So we can insert L=2w-4 into 2L+2w=34

2(2w-4)+2w=34

4w-8+2w=34

6w=42

w=7

If the width is 7, we can insert it into 2L+2w=34 to find out the length

2L+14=34

2L=20

L=10

The width is 7 ft, the length is 10 ft.

The length and width of the rectangle are 10 feet and 7 feet respectively. This is determined by setting up and solving equations based on the given information about the relationship between the length and width and the perimeter of the rectangle.

Given that the length (L) of the rectangle is 4 less than twice the width (W), we can represent this as:

L = 2W - 4

. We also know that the perimeter (P) of the rectangle is 34 feet. The formula for the perimeter of a rectangle is

P = 2L + 2W

. Substituting L in the perimeter equation gives

P = 2(2W - 4) + 2W = 34

. Simplifying the equation leads to

4W - 8 + 2W = 34

, and then

6W = 42

when you add 8 to both sides. Solving for W gives

W = 7 feet

. Substituting W = 7 into the length equation gives

L = 2(7) - 4 = 10 feet

. Therefore, the width and length of the rectangle are 7 feet and 10 feet respectively.

https://brainly.com/question/31677552

#SPJ3

Y-4X=-17 or -4x + y =-17

to convert it into standard from you first need to get X on the left, you can do that by subtracting x from both sides,

Answer:

-4x + y = -17

Step-by-step explanation:

The standard form of a linear equation is

ax + by = c

Your equation is

        y = 4x – 17     Subtract 4x from each side

-4x + y = -17

Answer:

9%

Step-by-step explanation:

1/11 students

1 divided by 11

=0.09090909090909

to convert the decimal to a percentage, multiply 100 to .09

9%

Answer:

-35%  

Step-by-step explanation:

To solve this equation, the first thing we have to do is to convert percentages to decimals because we are doing mathematical operations with a fraction.

To convert a percentage to a decimal, we just divide by 100. So, 60% equals 0.60, and 25% equals 0.25.

Next, we subtract these values from 1/2.

So, we have the following steps:

1. Calculate 1/2 - 0.60 (which is the decimal equivalent of 60%). This gives us -0.10.

2. Then subtract 0.25 (which is the decimal equivalent of 25%) from the result. So, -0.10 - 0.25 equals -0.35.

Therefore, 1/2 - 60% - 25% equals -0.35.

For this case, we must indicate which of the given functions is not defined for[tex]x = 0[/tex]

By definition, we know that:

[tex]f (x) = \sqrt {x}[/tex] has a domain from 0 to infinity.

Adding or removing numbers to the variable within the root implies a translation of the function vertically or horizontally. For it to be defined, the term within the root must be positive.

Thus, we observe that:

[tex]y = \sqrt {x-2}[/tex] is not defined, the term inside the root is negative when [tex]x = 0[/tex].

While [tex]y = \sqrt {x + 2}[/tex] if it is defined for [tex]x = 0.[/tex]

[tex]f(x)=\sqrt[3]{x}[/tex], your domain is given by all real numbers.

Adding or removing numbers to the variable within the root implies a translation of the function vertically or horizontally. In the same way, its domain will be given by the real numbers, independently of the sign of the term inside the root.

So, we have:

[tex]y = \sqrt [3] {x-2}[/tex] with x = 0: [tex]y = \sqrt [3] {- 2}[/tex] is defined.

[tex]y = \sqrt [3] {x + 2}[/tex]with x = 0: [tex]y = \sqrt [3] {2}[/tex]in the same way is defined.

Answer:

[tex]y = \sqrt {x-2}[/tex]

Option b

The function that are undefined for (x=0) is  [tex]y = \sqrt[3]{x-2}[/tex] and [tex]y = \sqrt{x-2}[/tex] and this can be determined by putting (x=0) in all the given expressions.

Given :

Function 1 - [tex]y = \sqrt[3]{x-2}[/tex]

Function 2 - [tex]y = \sqrt{x-2}[/tex]

Function 3 - [tex]y = \sqrt[3]{x+2}[/tex]

Function 4 - [tex]y = \sqrt{x+2}[/tex]

Evaluate each function at (x = 0) to determine which function is undefined for (x = 0).

Function 1 - [tex]y = \sqrt[3]{x-2}[/tex]

put (x = 0) in above function:

[tex]y = \sqrt[3]{-2}[/tex]

Therefore, it can be concluded that the above function is not defined for (x=0).

Function 2 - [tex]y = \sqrt{x-2}[/tex]

put (x = 0) in above function:

[tex]y = \sqrt{-2}[/tex]

Therefore, it can be concluded that the above function is not defined for (x=0).

Function 3 - [tex]y = \sqrt[3]{x+2}[/tex]

put (x = 0) in above function:

[tex]y = \sqrt[3]{2}[/tex]

Therefore, it can be concluded that the above function is defined for (x=0).

Function 4 - [tex]y = \sqrt{x+2}[/tex]

put (x = 0) in above function:

[tex]y = \sqrt{2}[/tex]

Therefore, it can be concluded that the above function is defined for (x=0).

For more information, refer to the link given below:

https://brainly.com/question/2263981

Answer:

option c

Step-by-step explanation:

Below are the 3 major determining factors to determine a good credit score:-

1) Payment history - The payment history comprises of 35 percent of the total credit score and is the most important factor in calculating credit scores. An easiest way for borrowers to improve their credit score is by making quick timely payments.

2) Credit utilization - It is the percentage of available credit which has been borrowed. It makes up 30 percent of the total credit scores.

3) Long-standing lines of credit - the amount of time each account has been open.It makes up 15 percent of the total credit score. In order to improve the credit scores, people without a credit history must begin using credit, and those having credit must maintain long-standing accounts.

Answer:

y=f(x)

y=5x

y=3x

are examples of function

Step-by-step explanation:

definition of a function

if there is one to one relation between a relation

then  it is defined as a function

for example

y=5x is a function

because when we put some value of x it gives back only one value of y as output.

y=±5x is  not a function because one value of x gives two values(positive and negative) values of y hence not a function.

The total number of seats in a row = 5

Lets suppose you are standing in front of the row, so you have 3 seats on one side of you then the passage of the plane and 2 seats on the other side. Out of 3 seats, 1 is window, 1 is middle and 1 is aisle. Similarly, out of the 2 seats on the other side, 1 is the window and 1 is aisle seat, Hence, a total of 5 seats.

As 2 friends have requested to be seated in the same row. So probability of them getting aisle seats becomes 2/5 for 1st friend (as there are 2 aisle seats out of 5 seats) and 1/4 (1 seat is already allocated to the friend so only 1 aisle seat is left out of 4 seats) for the second one.

So, joint probability becomes = [tex]\frac{2}{5}*\frac{1}{4}= \frac{1}{10}[/tex]

or probability becomes 0.1

Answer:

D. -17/2

Step-by-step explanation:

1/2 - 4 (1/2 + 1)^2

First we evaluate what is inside the parentheses

1/2 - 4  (3/2) ^2

Now we square what is inside the parentheses

1/2 - 4(9/4)

Now multiply

1/2 -9

Get a common denominator  9 = 9 *2/2 = 18/2

1/2 - 18/2

-17/2

Use PEMDAS:

P Parentheses first

E Exponents (ie Powers and Square Roots, etc.)

MD Multiplication and Division (left-to-right)

AS Addition and Subtraction (left-to-right)

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

[tex]\dfrac{1}{2}-4\left(\dfrac{1}{2}+1\right)^2=\dfrac{1}{2}-4\left(1\dfrac{1}{2}\right)^2=\dfrac{1}{2}-4\left(\dfrac{1\cdot2+1}{2}\right)^2\\\\=\dfrac{1}{2}-4\left(\dfrac{3}{2}\right)^2=\dfrac{1}{2}-4\cdot\dfrac{3^2}{2^2}=\dfrac{1}{2}-4\cdot\dfrac{9}{4}=\dfrac{1}{2}-1\cdot\dfrac{9}{1}\\\\=\dfrac{1}{2}-9=\boxed{-8\dfrac{1}{2}=-\dfrac{8\cdot2+1}{2}=\boxed{-\dfrac{17}{2}}}\to\boxed{D.}[/tex]

Answer:

The slope of the line is 3/4

Step-by-step explanation:

There is a difference of 3 in the y coordinate and 4 for the x coordinate from each exact point.

Answer:

5%

Step-by-step explanation:

(4.2- 4.0)/4.0 * 100 = 5%

Answer:

The percent of increase in the cost of gasoline, from May to June, is 5%.

Step-by-step explanation:

We were given the following:

In May the price of gasoline was $4.00 and in June the price went up to $4.20.

We can determine the percent increase as follows:

percentage increase in gasoline(%) = ((final price-original price)/final price)*100

let y be the final percentage increase of gasoline.

[tex]y=((4.2-4)/4.2)*100=5[/tex]

So the increase of gasoline as 5%

We can check this by multiplying the original prices by 5% and adding the original price.

[tex]4*0.05+4=4.2[/tex]

Answer:

-11/-16

Step-by-step explanation:

M= Y2 - Y1/ X2 - X1 = -9-(2)/ -7-(9) = -11/ -16

The slope of the line is 11/16.

The slope of any given formula can be found as

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

Where, y2 and y1 are the y-coordinates of the given two points

and, x2 and x1 are the x-coordinates of the given two points.

By the problem, y2 = -9 , y1 = 2 , x2 = -7 and x1 = 9

Using the above identity,

Slope = (-9 - 2) / (-7 - 9)

∴ Slope = -11 / -16 = 11/16 = 0.6875

Thus the slope of the line containing given points is 11/16

To learn more about slope of straight line, refer -

https://brainly.com/question/3493733

#SPJ2

-6x + 11 < -9x + 2

Add 9x to both sides.

3x + 11 < 2

Subtract 11 from both sides.

3x < -9

Divide both sides by 3.

x < -3

Answer:

A

Step-by-step explanation:

Answer:

[tex]a_n=A(n)=3n+3.[/tex]

Step-by-step explanation:

You are given recursive formula [tex]A(n)=A(n-1)+3,[/tex] where [tex]A(1)=6.[/tex]

Find some terms of the sequence:

[tex]a_1=A(1)=6,\\ \\a_2=A(2)=A(1)+3=6+3=9,\\ \\a_3=A(3)=A(2)+3=9+3=12,\\ \\a_4=A(4)=A(3)+3=12+3=15,...[/tex]

You van see that these terms form the arithmetic sequence with first term [tex]a_1=6[/tex] and difference [tex]d=3.[/tex]

An explicit formula for n-th term of arithmetic sequence is

[tex]a_n=a_1+(n-1)d.[/tex]

In your case,

[tex]a_n=6+(n-1)\cdot 3,\\ \\a_n=6+3n-3,\\ \\a_n=3n+3.[/tex]

Subtract the cost of the pencils from the total cost. This will be he amount she spent on erasers. Then divide that amount by the cost of each eraser to get the total.

4.25 - 1.75 = 2.50 spent on erasers

2.50 / 0.25 = 10

She bought 10 erasers.

Answer: B

Step-by-step explanation:

Answer:

a progression is a summation of quantities based upon a sequence.

Step-by-step explanation:

example of a progression

1,4,7,10,13,16,.........

a1=1

a2=4

a3=7

difference =d=a2-aq=4-1=3

similarly

d=a3-a2=7-4=3

we can clearly see that there is a difference of 3 between two consecutive terms of a progression

on the other hand successive terms of a progression can be obtained by adding a unique value in backward term to get successive term.

hence a progression is   a summation of quantities based upon a sequence

Answer:

A summation of quantities based upon a sequence, and an arrangement of quantities whose positions are based upon the natural numbers

Step-by-step explanation:

It cannot be "Any list of numbers" because a progression only contains natural numbers, meaning no decimals or fractions. It is also not a new discovery in mathematics.  

[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2,\ \text{then}\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\-------------------------\\\\\text{We have}\ 5x+3y=8\qquad\text{subtract 5x from both sides}\\\\3y=-5x+8\qquad\text{divide both sides by 3}\\\\y=-\dfrac{5}{3}x+\dfrac{8}{3}\to m_1=-\dfrac{5}{3}\\\\\text{Therefore}\ m_2=-\dfrac{1}{-\frac{5}{3}}=\dfrac{3}{5}\\\\Answer:\ \boxed{b.\ \dfrac{3}{5}}[/tex]

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

[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2,\ \text{then}\\\\l\ \parallel\ k\iff m_1=m_2\\\\\text{We have}\ 3x-5y=10\qquad\text{subtract 3x from both sides}\\\\-5y=-3x+10\qquad\text{divide both sides by (-5)}\\\\y=\dfrac{3}{5}x-2\to m_1=\dfrac{3}{5}\\\\\text{Therefore we have}\ m_2=\dfrac{3}{5}.\\\\Answer:\ \boxed{D.\ y=\dfrac{3}{5}x}[/tex]

Answer:

Answer Left Panel: 3/5 or B

Answer Right Panel: D

Step-by-step explanation:

Left Panel

Right Panel

The slope of a line parallel to another line is the same as the given line.

Answer: 42 inch 16:9 television

Step-by-step explanation:

The dimensions of 42 inch 16:9 television are:

Width of the television = 36.6 inches

Height of the television = 20.6 inches

Screen Area of the television = 36.6 x 20.6 = 753.96 sq inches

The dimensions of 32 inch 4:3 television are:

Width of the television = 25.6 nches

Height of the television = 19.2 inches

Screen Area of the television = 25.6 x 19.2 = 491.52 sq inches

Thus 42 inches 16:9 television has 262.44 square inches more screen area.

Hope it helps.

Thanks you :)

[tex]\text{Look at the picture.}[/tex]

[tex]x, y - some\ units\ of\ leng th[/tex]

[tex]\text{Use the Pythagorean theorem:}[/tex]

[tex](16x)^2+(9x)^2=42^2\\\\256x^2+81x^2=1764\\\\337x^2=1764\qquad\text{divide both sides by 337}\\\\x^2=\dfrac{1764}{337}\to x=\sqrt{\dfrac{1764}{337}}[/tex]

[tex]\text{The area:}\\\\A_1=16\sqrt{\dfrac{1764}{337}}\cdot9\sqrt{\dfrac{1764}{337}}=(16)(9)\left(\sqrt{\dfrac{1764}{337}}\right)^2\\\\=144\cdot\dfrac{1764}{337}\approx754\ in^2[/tex]

[tex](4x)^2+(3x)^2=32^2\\\\16x^2+9x^2=1024\\\\25x^2=1024\qquad\text{divide both sides by 25}\\\\x^2=40.96\to x=\sqrt{40.96}\to x=6.4\ in\\\\\text{The area:}\\\\A_2=4(6.4)\cdot3(6.4)=25.6\cdot19.2=491.52\ in^2[/tex]

[tex]754 > 491.52[/tex]

Answer:

$300

Step-by-step explanation:

Let Dave's saving be D and Sam's savings be S

[tex]\frac{D}{S}=\frac{5}{4}\\4D=5S\\\frac{4}{5}D=S[/tex]

So we subtract 40 from each of them and then the ratio becomes 13 is to 10. Hence we can write:

[tex]\frac{D-40}{S-40}=\frac{13}{10}\\10(D-40)=13(S-40)\\10D-400=13S-520\\-400+520=13S-10D\\120=13S-10D[/tex]

Plugging in [tex]\frac{4}{5}D[/tex] into S (as we found earlier), we can solve for D (our answer):

[tex]120=13S-10D\\120=13(\frac{4}{5}D)-10D\\120=\frac{52}{5}D-10D\\120=\frac{2}{5}D\\D=\frac{120}{\frac{2}{5}}=120*\frac{5}{2}=300[/tex]

So, Dave's savings at first, D, is $300.

The -30 does not matter in this case because it does not affect the slope. So, you can ignore it and simplify the question to 5x-7y=0.

Move the -7y to the right to get 5x=7y. Then, divide by 7 to isolate y to get y=5x/7.

Therefore, the slope is 5/7.  

Final answer:

The slope of the graph of the line 5x - 7y = -30 is 5/7, determined by rewriting the equation in the slope-intercept form and identifying the coefficient of the x term as the slope.

Explanation:

To find the slope of the graph of the line given by the equation 5x - 7y = -30, we need to rewrite the equation in the slope-intercept form, which is y = mx + b, where m is the slope, and b is the y-intercept. Starting with the given equation:

5x - 7y = -30

-7y = -5x - 30

y = (5/7)x + 30/7

From the transformed equation y = (5/7)x + 30/7, we can see that the slope (m) is 5/7. This means that for every one-unit increase in the independent (x) variable, the dependent (y) variable increases by 5/7 units.

Answer:

A. 3/8

Step-by-step explanation:

Step 1. Change the denominators so they are the same value

1/2 x 4 = 4/8

Step 2. Compare

3/8 < 4/8

Answer:

A. [tex]\dfrac{3}{8}[/tex] is smaller than [tex]\dfrac{1}{2}[/tex].

Step-by-step explanation:

The given fraction is [tex]\dfrac{1}{2}[/tex].

To compare two fractions, either numerator or denominator should be equal.

It is required to compare the given fraction with [tex]\dfrac{3}{8}[/tex] and [tex]\dfrac{5}{8}[/tex].

Now, the given fraction can be written as,

[tex]\dfrac{1}{2}\times\dfrac{4}{4}=\dfrac{4}{8}[/tex]

Now, the denominator of the given fraction is equal to that of other fractions.

In the fraction [tex]\dfrac{3}{8}[/tex] , numerator 3 is smaller than that of the given fraction which is 4.

So, the fraction [tex]\dfrac{3}{8}[/tex]  is smaller than [tex]\dfrac{1}{2}[/tex].

In the fraction [tex]\dfrac{5}{8}[/tex] , numerator 4 is larger than that of the given fraction which is 4.

So, the fraction  [tex]\dfrac{5}{8}[/tex] is larger than [tex]\dfrac{1}{2}[/tex].

Therefore, A. [tex]\dfrac{3}{8}[/tex] is smaller than [tex]\dfrac{1}{2}[/tex].

For more details, refer the link:

https://brainly.com/question/20026594?referrer=searchResults

Answer:

13/7

Step-by-step explanation:

Simply add the slices!

3+2+3+5=13 Slices

Now, we know that a full pie is 7 slices, and the answer they want is a fraction of a whole pie. Simply put the slices we have over how many are in a whole pie.

Answer: 13/7

This means we have almost 2 pies worth of random leftover slices :)

Answer:

Approximately  1.9 seconds   (correct to nearest tenth)

Step-by-step explanation:

Looks like the function is  d = -16t^2 + 55    ( you left out the t)

The answer is the value of t when d = 0 so we have the equation:-

0 =  -16t^2 + 55

16t^2 = 55

t^2 = 55/16

t = sqrt (55/16)

= 1.85 seconds

Answer:

t is approximately 1.854049622 seconds

Step-by-step explanation:

d = -16 t^2 + 55

Let d = 0

0 = -16 t^2 + 55

Subtract 55 from each side

-55 = -16 t^2

Divide by -16 on each side

-55/-16 =  -16 /-16t^2

55/16 = t^2

Take the square root of each side

sqrt(55/16) = sqrt(t^2)

We only take the positive square root because time must be positive

sqrt(55/16) = t

t is approximately 1.854049622 seconds

Answer:

F(-1/2)= 5 1/3

Step-by-step explanation:

-1/2 X -2/3 = 1/3 because the two negatives cancle out. 1/3 + 5=

5 and 1/3.

Answer:

5 1/3

Step-by-step explanation:

9y + 6 = 9 + 2y + 2y

9y + 6 = 9 + (2y + 2y)

9y + 6 = 9 + 4y      subtract 6 from both sides

9y = 3 + 4y     subtract 4y from both sides

Answer:

5y = 3

Step-by-step explanation:

9y + 6 = 9 + 2y + 2y

9y + 6 = 9 + (2y + 2y)

9y + 6 = 9 + 4y      subtract 6 from both sides

9y = 3 + 4y     subtract 4y from both sides

5y = 3

Answer:

1.0

Step-by-step explanation:

The answer is 1.0 It is not a tenth but 99 is closer to 100. witch is 1.0 Do you try looking it up. This is a site i used. It is great. It is called calculator soup.

Answer: A formula that can be used to find the answer is (x Squared = 110.25) So (x times x = 110.25) 10.5 is the length of one side because 10.5 squared = 110.25.

Answer is 10.5

Final answer:

To find the length of one side of Mickey’s square-shaped office with an area of 110.25 square feet, we take the square root of the area, resulting in a side length of 10.5 feet.

Explanation:

The question asks for the length of one side of Mickey’s square-shaped office given that the area of the office is 110.25 square feet. To find the length of one side, we can use the formula for the area of a square, which is area = side², where ‘side’ represents the length of one side of the square. Given that the area = 110.25 ft², we solve for the side length by taking the square root of the area.

So, the calculation would be side = √(110.25 ft²), which equals 10.5 feet. Therefore, the length of one side of Mickey’s square office is 10.5 feet.

Answer:

Given: Scale factor, [tex]k = \frac{1}{4}[/tex] and centered at (5, -5).

Labelled the given figure as A, B and C.

The coordinates of the given triangle ABC are;

A = (-3, 7)

B = (-7, -5) and

C = (9, 3)

To find the image of the figure after a dilation with scale factor 1/4 centered at (5, -5).

The rule of dilation with scale factor 1/4 and centered at (5, -5) is given by;

[tex](x, y) \rightarrow (\frac{1}{4} (x -5) +5 , \frac{1}{4}(y+5) -5)[/tex]

or

[tex](x, y) \rightarrow (\frac{1}{4}x + \frac{15}{4}, \frac{1}{4}y -\frac{15}{4})[/tex]

The coordinates of the image of the figure after dilation are;

[tex]A(-3, 7) \rightarrow (\frac{1}{4}(-3) + \frac{15}{4}, \frac{1}{4}(7)-\frac{15}{4})=(\frac{-3}{4}+ \frac{15}{4}, \frac{7}{4}- \frac{15}{4}) = (\frac{-3+15}{4}, \frac{7-15}{4}) = (\frac{12}{4}, \frac{-8}{4}) = A'(3, -2)[/tex]

[tex]B(-7, -5) \rightarrow (\frac{1}{4}(-7) + \frac{15}{4}, \frac{1}{4}(-5)-\frac{15}{4})=(-\frac{7}{4}+ \frac{15}{4}, -\frac{5}{4}- \frac{15}{4}) = (\frac{-7+15}{4}, \frac{-5-15}{4}) = (\frac{8}{4}, \frac{-20}{4}) = B'(2, -5)[/tex]

[tex]C(9, 3) \rightarrow (\frac{1}{4}(9) + \frac{15}{4}, \frac{1}{4}(3)-\frac{15}{4})=(\frac{9}{4}+ \frac{15}{4}, \frac{3}{4}- \frac{15}{4}) = (\frac{9+15}{4}, \frac{3-15}{4}) = (\frac{24}{4}, \frac{-12}{4}) = C'(6, -3)[/tex]

As,You can see the graph as shown below in the attachment.

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have m = 2 and the points (1, 2) and (3, y). Substitute:

[tex]\dfrac{y-2}{3-1}=2\\\\\dfrac{y-2}{2}=2\qquad\text{multiply both sides by 2}\\\\y-2=4\qquad\text{add 2 to both sides}\\\\\boxed{y=6}[/tex]