The width of a rectangle is 3 less than its length find the width of the rectangle if its perimeter is 26ft

Answer:

$16.60

Step-by-step explanation:

Setup the formula to calculate the cost of each pound of salmon and swordfish for the 2.5 pounds of salmon (x) and 1.25 pounds of swordfish (y) which is equal to $31.25

2.5x + 1.25y = 31.25

Setup a formula to figure out how much a single pound of swordfish (y) is. The problem states it cost $0.20 less than a pound of salmon (x).

y = x - .20

Plug the y = x - .20 into the first equation.

2.5x + 1.25(x - .20) = 31.25

Distribute the 1.25 by multiplying it with x and -.20

2.5x + 1.25x - .25 = 31.25

Combine like terms, x on the left side

3.75x - .25 = 31.25

Add .25 to both sides to get x on one side

3.75x = 31.50

Divide both sides by 3.75 to get x by itself

x = 8.4

So, each pound of salmon, x, cost $8.40 per pound

Use y = x - .20 and plug in x = 8.4 to figure out how much a pound of swordfish cost.

y = 8.4 - .20

So, a pound of swordfish cost $8.20 per pound

The question wants to know the combined cost, z, of 1 pound of salmon, x, and 1 pound of swordfish, y.

x + y = z

8.4 + 8.2 = 16.6

The combined cost of 1 pound of salmon and 1 pound of swordfish is $16.60

Answer:

Step-by-step explanation:

z=9(x+2)

z=9x+18

Subtract 18 from both sides

z-18=9x+18-18

z-18=9x

Divide both sides by 9

z-18/9 =x

Therefore

X= z-18/9

Answer:

¹/₄

Step-by-step explanation:

Given:

The dessert is the "whole", i.e. equal to 1.

To find how much of the dessert was left, subtract all the given portions from 1:

[tex]\begin{aligned}\textsf{Dessert left for Sara} & = 1-\dfrac{1}{8}-\dfrac{1}{4}-\dfrac{3}{8}\\\\& = \dfrac{8}{8}-\dfrac{1}{8}-\dfrac{2}{8}-\dfrac{3}{8}\\\\& = \dfrac{8-1-2-3}{8}\\\\& = \dfrac{2}{8}\\\\& = \dfrac{1}{4}\end{aligned}[/tex]

Therefore, ¹/₄ of the dessert was left for Sara.

Answer:

2/8 (or) 1/4

Step-by-step explanation:

The amount of desert she served is,

→ 1/8 + 1/4 + 3/8

→ (1 + 2 + 3)/8

→ 6/8

Then amount of desert left for Sara is,

→ 1/1 - 6/8

→ (8 - 6)/8

→ 2/8 (or) 1/4

Hence, she was left with 2/8 of desert.

A line has no thickness, but it does have direction and infinite length.

A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions.

Given the variety of geometries in modern mathematics, the idea of a line is directly related to how the geometry is described. For instance, a line in the plane is frequently defined in analytic geometry as the collection of points whose coordinates satisfy a given linear equation, but in a more abstract context, such as incidence geometry, a line may be an independent object, distinct from the collection of points that lie on it.

In cartesian plane the general equation of a line is given by :

y=mx+c where the slope is denoted by m and the y-intercept by c.

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Answer:

45%

Step-by-step explanation:

1,450 - 1,000 = 450

the 450 becomes 0.45

to make 0.45 a percent, we multiply it by 100

0.45 x 100 = 45

45%

Solving a system of equations we can see that we need to use 120 ml of the 80% solution, and the other 80ml are of the 50% solution.

Let's define the variables:

We know that we want to make 200ml, then:

x  + y = 200

And the concentration of these 200ml must be of 68%, then the concentrations in the left side and in the rigth side must give the same value, so we can write:

x*0.5 + y*0.8 = 200*0.68

(the concentrations are written in decimal form)

Then we have the system of equations:

x  + y = 200

x*0.5 + y*0.8 = 200*0.68

To solve it we start by isolating x in the first equation:

x = 200 - y

Replacing that in the other equation we get:

(200 - y)*0.5 + y*0.8 = 200*0.68

Now we can solve this for y, we will get:

100 - y*0.5 + y*0.8 = 136

y*0.3 = 136 - 100 = 36

y = 36/0.3 = 120

So we need to use 120 ml of the 80% solution, and the other 80ml are of the 50% solution.

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The values of the composite functions are (f.g)(x) = 2x^3 - 19x^2 + 40x + 25 and (f/g)(x) = 2x + 1

The functions are given as:

f(x) = 2x^2 - 9x - 5

g(x) = x - 5

The composite function (f.g)(x) is calculated as

(f.g)(x) = f(x) * g(x)

This gives

(f.g)(x) = (2x^2 - 9x - 5) * (x - 5)

Evaluate the product

(f.g)(x) = 2x^3 - 9x^2 - 5x - 10x^2 + 45x + 25

Evaluate the like terms

(f.g)(x) = 2x^3 - 19x^2 + 40x + 25

The composite function (f/g)(x) is calculated as

(f/g)(x) = f(x)/g(x)

This gives

(f/g)(x) = (2x^2 - 9x - 5)/(x - 5)

Factorize the numerator

(f/g)(x) = (2x + 1)(x - 5)/(x - 5)

Evaluate the quotient

(f/g)(x) = 2x + 1

Hence, the values of the composite functions are (f.g)(x) = 2x^3 - 19x^2 + 40x + 25 and (f/g)(x) = 2x + 1

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Each part of the question is plotted on the number line as an image with the solution.

How are rational numbers represented on the number line?

(1)      [tex]\frac{-3}{8} , 1\frac{1}{5} = \frac{6}{5} = 1.2 , \frac{-3}{4}[/tex]  are plotted on the number line as an image with the solution.

(2) -13+15+(-8) = -6 is plotted on the number line as an image with the solution.

(3) [tex]\frac{3-(-14)}{7} = \frac{17}{7} = 2.429, \frac{-36+58}{-11} = -2[/tex] are plotted on the number line as an image with the solution.

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Answer:$976

Step-by-step explanation:

Answer:--------X=3/13---------

Step-by-step explanation:

Answer:

Image 2: a segment from -4 to 4 with the endpoints excluded (with empty circles).

Step-by-step explanation:

|x| < 4 means "the distance from x to 0 is less than 4". That means that any number bigger than -4 and smaller than 4 matches the inequality from the question.

Side note: Please start analyzing the absolute values as "distance from 0" and you'll be able to solve those questions yourself with less effort.

Answer: 125

Step-by-step explanation:

The total number of matches played is 552.

Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangments is called a combination.

The given parameters are as;

Teams = 24

Matches against each other = 2

Therefore, the total number of matches played is;

Total = Teams * (Teams - 1)

This gives;

Total = 24 * (24 - 1)

Evaluate;

Total = 552

Hence, the total number of matches played is 552.

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7+(-1) = -3

Steps of adding 7+(-10) using number line are as following:

1) Draw a number line by ranging from -10 to +10.

2) Point out 7 on the number line.

3) Because -10 is added to 7 on the number line, please move 10 numbers left to 7 on the number line. We always go left in addition of a negative number on the number line.

4) The number we reach -3 on left side would be our final sum.

5) From the number we can clearly see that moving 10 number on left to 7, we get -3.

Note: We are moving left because of negative sign in front of 10.

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Answer:

Step-by-step explanation:

first let : x = 3 and y = 5

so x-3 means 3-3 = 0

and 2y means 2 * 3 = 6

therfore x-3 > 2y means 0 > 6, false

Answer:

4/5

Step-by-step explanation:

8/10

=4/5

Answer:

8/9!!

all credit goes entirely to the person in comments for giving us all the right answer.

The two points on the y axis that are 25 units from (-24,3) will be (0, 10) and (0, - 4).

We are given a point:

( - 24 , 3 )

We need to find a point on the y - axis, that is 25 units away from the axis.

The coordinate of the point will be:

(0, y)

So, by using the distance formula, we get that:

D = √ ( y₂ - y₁)² + ( x₂ - x₁)²

25 = √ ( y + 3)² + (0 + 24)²

625 = y² + 9 - 6 y + 576

625 = y² - 6 y + 585

y² - 6 y - 40 = 0

y² - 10 y + 4 y - 40 = 0

y ( y - 10 ) + 4 ( y - 10 ) = 0

(y - 10)(y + 4) = 0

y = - 4 or y = 10.

So, the two points will be:

(0, 10) and (0, - 4)

Therefore, we get that, the two points on the y axis that are 25 units from (-24,3) will be (0, 10) and (0, - 4).

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Answer:

20%

Step-by-step explanation:

Every fifth car would be 1/5 or 20%

Answer:

x² + (y + 3)² = 25

Step-by-step explanation:

the centre (C) of the circle is at the midpoint of the diameter.

using the midpoint formula

midpoint = ( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

with (x₁, y₁ ) = P (3, 1 ) and (x₂, y₂ ) = Q (- 3, - 7 )

C = ( [tex]\frac{3-3}{2}[/tex] , [tex]\frac{1-7}{2}[/tex] ) = ( [tex]\frac{0}{2}[/tex] , [tex]\frac{-6}{2}[/tex] ) = (0, - 3 )

the radius r is the distance from the centre to either P or Q

using the distance formula

r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = C (0, - 3 ) and (x₂, y₂ ) = P (3, 1 )

r = [tex]\sqrt{(3-0)^2+(1-(-3)^2}[/tex]  

 = [tex]\sqrt{3^2+(1+3)^2}[/tex]

 = [tex]\sqrt{3^2+4^2}[/tex]

 = [tex]\sqrt{9+16}[/tex]

 = [tex]\sqrt{25}[/tex]

 = 5

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (0, - 3 ) and r = 5 , then

(x - 0 )² + (y - (- 3) )² = 5² , that is

x² + (y + 3)² = 25

Answer:

a)

sin30=high of steps/175

sin30=1/2

so

high of steps= 175/2

high of steps=87.5cm

b)

cos30=wide/175

cos30=3^1/2÷2

wide=175*3^1/2÷2

3^1/2=1.73

so

wide=175*1.73/2

wide=151.37

Answer: -4 because 2(-6)2 = -24 and 5(2)2 = 20 so -24 + 20 is -4.

Answer:-4

Step-by-step explanation:

2(-6)2

2 x -6 x 2=-24

5 x 2 x 2=20

-24+20=-4

Answer:

Area of Desert 1 = 12,000,000     Area of Desert 2 = 3,000,000

Step-by-step explanation:

x+y=15,000,000

x=4y

4y+y=15,000,000

5y=15,000,000

y=3,000,000

The mean of the data is 30 and the median of the data is 27.5.

Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data. The mean of the data will be calculated by adding all the numbers and dividing it by the quantity of the numbers.

The median of the data generally refers to the middle most value of the series. The median of the data is calculated by arranging the numbers in increasing order and getting the middle value of the numbers.

Given data is 26, 29, 27, 28, 29, 27, 27, 53, 25, 29 arrange all the numbers in increasing order.

25,26,27,27,27,28,29,29,29,53

Mean = Sum of all the numbers / Total numbers

Mean =  (25 + 26 + 27 + 27 + 27 + 28 + 29 + 29 + 29 + 53 ) / 10

Mean = 300 / 10

Mean = 30

Median = ( 27 + 28 ) / 2 = 27.5

Therefore, the mean of the data is 30 and the median of the data is 27.5.

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The numeric values for the functions are given as follows:

6 - a) f(-2) = -13.

6 - b) g(4) = 11.

To find the numeric value of a function, we replace each instance of the variable by the desired value.

At item 6a, the function is given by:

f(x) = 5x - 3.

The numeric value at x = -2 is:

f(-2) = 5(-2) - 3 = -10 -3 = -13.

Hence f(-2) = -13.

At item 6b, the function is given by:

g(x) = 0.5x² + 3.

The numeric value at x = 4 is:

g(4) = 0.5(4)² + 3 = 8 + 3 = 11.

Hence g(4) = 11.

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Step-by-step explanation:

It's simple in the following diagram ( 13x + 45)° + (19x +3)° won't be equal to 180° as they are vertically opposite angle...... and are vertically opposite to each other...

So to find the value of x :

13x + 45° = 19x + 3°

13x - 19x = 3 - 45

-6x = - 42

x = -42 / -6

x = 7°

☘☘☘...

Answer: x=0.5, y=1

Step-by-step explanation:

-4x+3y=1

6x-y=2

6x-2=y

-4x+3(6x-2)=1

-4x+18x-6=1

-4x+18x=7

14x=7

x=0.5

6x-y=2

6(0.5)-y=2

3-y=2

y=1

Let's change the equation,

→ 6x - y = 2

→ y = 6x - 2

Then the value of x will be,

→ -4x + 3y = 1

→ -4x + 3(6x - 2) = 1

→ -4x + 18x - 6 = 1

→ 14x = 1 + 6

→ x = 7/14

→ [ x = 1/2 ]

Hence, the value of x is 1/2 (or) 0.5.

Now the value of y will be,

→ y = 6x - 2

→ y = 6(1/2) - 2

→ y = 3 - 2

→ [ y = 1 ]

Hence, the value of y is 1.

Answer:

6

Step-by-step explanation:

6 x 6 = 36