Which equation represents the line shown on the graph?

Answer:

Let y represents the ounces of first spice.

From the given statements, we draw a table as shown below:

                          ounces of spice        Percentage          ounces of salt

First spice                 y                              3%                            0.03x

Second spice           175                            6%                          175(0.06)

Final  mixture          y + 175                         5%                        (x+15)(0.05)

Now, to solve for y

we have;

Final spice = First spice + second spice

[tex]0.03y + 175(0.06) = (y+175)(0.05)[/tex]

[tex]0.03y+ 10.5= 0.05y+ 8.75[/tex]

Subtract 10.5 on both sides we have;

[tex]0.03y+ 10.5 -10.5= 0.05y+ 8.75 -10.5[/tex]

Simplify:

[tex]0.03y = 0.05y -1.75[/tex]

Subtract 0.05y on both sides

[tex]0.03y -0.05y= 0.05y -1.75-0.05y[/tex]

Simplify:

[tex]-0.02y = -1.75[/tex]

Divide both sides by -0.02, we get;

[tex]y = \frac{-1.75}{-0.02} = 87.5[/tex]

Therefore, 87.5 ounces of spices that is 3% salt should be added to 175 ounces of a spice that is 6% salt in order to make a spice that is 5% salt

It needs 87.5 ounces of spice that is 3% salt.

Order of Operations in Mathematics follow this following rule :

This rule is known as the PEMDAS method.

In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.

Let us tackle the problem !

[tex]\texttt{ }[/tex]

Given:

175 ounces of a spice that is 6% salt

[tex]\texttt{mass of salt from this spice} = s_1 = 6\% \times 175 = 10,5 \texttt{ ounces}[/tex]

[tex]\texttt{ }[/tex]

x ounces of a spice that is 3% salt

[tex]\texttt{mass of salt from this spice} = s_2 = 3\% \times x = 0.03x \texttt{ ounces}[/tex]

[tex]\texttt{ }[/tex]

(175 + x) ounces of a spice that is 5% salt

[tex]\texttt{total mass of salt} = s_1 + s_2[/tex]

[tex]5\% \times ( 175 + x ) = 10.5 + 0.03x[/tex]

[tex]8.75 + 0.05x = 10.5 + 0.03x[/tex]

[tex]0.05x - 0.03x = 10.5 - 8.75[/tex]

[tex]0.02x = 1.75[/tex]

[tex]x = 1.75 \div 0.02[/tex]

[tex]x = 175 \div 2[/tex]

[tex]x = 87.5 \texttt{ ounces}[/tex]

[tex]\texttt{ }[/tex]

Grade: Middle School

Subject: Mathematics

Chapter: Percentage

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent , cookies , chocolate , chip , paper , fourth , pieces , Number , 51 , 33 , 1/3

Answer:

The equation would be y = -4/7x - 1

Step-by-step explanation:

Given that we have the slope and the point, we can solve for the equation using point-slope form.

y - y1 = m(x - x1)

y + 5 = -4/7(x - 7)

y + 5 = -4/7x + 4

y = -4/7x - 1

The equation that represents a line that passes through the point (7,-5) and has a slope of -4/7 is,

⇒ 7y = - 4x - 7

The equation of a line in point-slope form passing through the point

(x₁ , y₁) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Given that,

The equation of line passes through the point (7,-5) and has a slope of -4/7.

Here we have,

[tex](x_1 , y_1) = (7, - 5)[/tex]

And, [tex]m = \frac{- 4}{7}[/tex]

Substitute the given values in the above equation,

[tex]y - y_1 = m (x - x_1)[/tex]

[tex]y - (- 5) = \frac{-4}{7} (x - 7)[/tex]

[tex]y + 5 = \frac{-4}{7} (x - 7)[/tex]

Multiply by 7 on both sides,

[tex]7 (y + 5) = - 4 (x - 7)\\7y + 35 = - 4x + 28\\ 7y =- 4x 28 - 35\\ 7y = - 4x- 7\\[/tex]

So, the equation of a line is,

7y = - 4x - 7

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Answer:

Constant of proportionality,  [tex]r = \frac{1}{10}[/tex]

Step-by-step explanation:

Constant of proportionality states that the constant value of the ratio of two proportional quantities x and y,

it is written in the form of y = kx, where k is the constant of proportionality.

Given the equation: [tex]y =rx[/tex]                        .....[1]

where r is the constant of proportionality.

From the table we consider

x = 14 and y = 1.4

Substitute these given values in [1] to solve for r;

[tex]1.4 = r(14)[/tex]

Divide both sides by 14 we get;

[tex]r = \frac{1.4}{14} = \frac{14}{140} = \frac{1}{10}[/tex]

therefore, the Constant of proportionality,  [tex]r = \frac{1}{10}[/tex]

The constant of proportionality, denoted as 'r', represents the ratio between the dependent variable (y) and the independent variable (x) in a linear equation. It determines the rate of change of y with respect to x.

The constant of proportionality, denoted as 'r', represents the ratio between the dependent variable (y) and the independent variable (x) in a linear equation. It determines the rate of change of y with respect to x. For example, in the equation y = rx, 'r' represents how much y changes for every unit change in x.

For instance, if the equation is y = 2x, then the constant of proportionality is 2. This means that for every unit increase in x, y increases by 2 units.

Keywords: constant of proportionality, linear equation, rate of change

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Answer:

B' = (-8,-1) , C' = (4, 5)

Step-by-step explanation:

The coordinates  of A are (-5,-7)

The coordinates of C are  3 units to the right and 4 up from A.

So for a dilation  factor 3 C' will be 9 to the right and 12 up from A.

C' = (-5 + 9) , (-7 + 12)

=  (4, 5).

The point B is 1 unit to left and 2 up from A.

So B' is (-5 -3) , (-7+ 6)

= (-8, -1).

After a dilation scale factor of 3 centered at A, B'(- 18, - 15), and C'(- 6, - 9).

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

Given, A triangle ABC.

The coordinate of B is (- 6, - 5), and the coordinate of C is (- 2, - 3).

After a dilation scale factor of 3 centered at A coordinates of B' would be

(- 6×3, - 5×3) = (- 18, - 15) and C'(- 2×3, - 3×3) = (- 6, - 9).

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If Javier starts with a higher initial balance of $300, the initial point on his savings graph would be higher by $100, and all subsequent points would reflect this initial increase, though the slope of the graph would remain unchanged.

If Javier opens a savings account with a starting balance of $300 instead of $200 and then deposits $75 each week, the graph representing his savings over time would change in the following way:

The initial point on the graph, representing the starting balance, would be higher.

This is because the starting balance would be $300 instead of $200.

After this initial change, the slope of the graph, representing the weekly deposits of $75, would remain the same.

However, every point on the graph after the initial deposit would be $100 higher than it was before because each point on the savings graph accumulates the effects of the higher starting balance.

The point-slope form of a line:

[tex]y-y_1=m(x-x_1)[/tex]

We have the slope m = -4 and the point (8, -7). Substitute:

[tex]y-(-7)=-4(x-8)[/tex]     use distributive property

[tex]y+7=-4x+32[/tex]      subtract 7 from both sides

[tex]y=-4x+25[/tex]      add 4x to both sides

[tex]\boxed{4x+y=25}[/tex]

To make the statement '17/20 ? -11.95' true, the correct symbol to use is '>'. We find this by comparing the result of 17 divided by 20 (which is 0.85) with -11.95.

The question is asking us to find the correct sign (either less than '<', equal '=', or greater than '>') to make the mathematical statement '17/20 ? -11.95' true.

To solve this, we first need to divide 17 by 20 to get 0.85. Then, we compare this result with -11.95.

Since 0.85 is greater than -11.95, we use the '>' symbol. Thus, the statement '17/20 > -11.95' is true.

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Answer:

3030.033

Step-by-step explanation:

Multiply each piece out and add them together

3 X 1,000 + 3 X 10 + 3 X 1/100 + 3 in X 1/1000

3000 + 30+.03 + .003

3030.033

Answer:

17

Step-by-step explanation:

15.92 is close to 16

0.85 is close to 1

15.92 + 0.85 is close to 16 + 1

16 + 1 = 17

15.92 + 0.85 is approximately 17

The point-slope form:

[tex]y-y_1=m(x-x_1)[/tex]

We have m = -4 and the point (-2, 5). Substitute:

[tex]y-5=-4(x-(-2))[/tex]

[tex]y-5=-4(x+2)[/tex]      use distributive property

[tex]y-5=(-4)(x)+(-4)(2)[/tex]

[tex]y-5=-4x-8[/tex]      add 5 to both sides

[tex]\boxed{y=-4x-3}[/tex]

Answer:

all is work is shown and pictured

Answer:

y = - 3

Step-by-step explanation:

Providing you mean (y - 9)/(y + 3) then it is always the variable in the denominator that is going to cause trouble. If it equals zero at any point, it's game over.

It's a little better if you get a result like 0/0. That problem has a "depends" as an answer, but by and large, you don't want to monkey around with 0 in the bottom of a fraction.

y + 3 = 0            Subtract 3 from both sides.

y + 3 - 3 = 0 - 3  Combine

y = - 3

Answer:

9/20

Step-by-step explanation:

9/10 times 1/2 equals 9/20

Answer:

9/20

Step-by-step explanation:

Answer:

$18 034.42

Step-by-step explanation:

The formula for the future value of an account paying 5 % annual interest compounded quarterly for four years is

[tex]A = P(1 +\frac{r }{n })^{nt}[/tex]

A = $22 000

r = 0.05

n = 4 times per year

t = 4 years

[tex]22 000 = P(1 +\frac{0.05 }{4 })^{4\times4}[/tex]

[tex]22 000 = P(1 + 0.0125)^{16}[/tex]

[tex]22 000 = P(1.0125)^{16}[/tex]

22 000 = P x 1.220

P = 2 000/1.220

P = $18 034.42

You must invest $18 034.42.

Answer:

[tex]\frac{a-5}{4}[/tex]

Step-by-step explanation:

the given equation is

[tex]\frac{a-5}{a} /\frac{4}{a}[/tex]

from the multiplication rules we know that

[tex]\frac{a}{b}/\frac{c}{d}=\frac{a}{b}*\frac{d}{c}[/tex]

so for the given equation changing the sidn of division to multiplication

the equation becomes

[tex]\frac{a-5}{a} * \frac{a}{4}[/tex]

a cancels out from both numerator and denominator

so it becomes

[tex]\frac{a-5}{4}[/tex]

which is the answer

Answer:

20%

Step-by-step explanation:

We can say that 3/15 students usually go to bed at 9 P.M. We can set up a proportion to solve this problem.

3/15=x/100

We cross multiply to find x

15x=300

Divide both sides by 15

x=20

So 20% of the classmates usually sleep at 9 P.M.

Answer:

20% of the students

Step-by-step explanation:

(4, 2) (-4, -2)

Slope is the change in Y over the change in X

From the two points given:

Slope =( -2 - 2 ) / ( -4 -4)

Slope = -4 / -8

Slope = 1/2

m = 1/2

Answer: about 15.72

Step-by-step explanation: i used a calculator

Answer:

Given: Ellentown college has approximately 3 times 10 to the 3 power students and pengrove university approximate 30,000 students.

⇒ number of students approximately in Ellentown college = [tex]3 \times 10^3[/tex]

also,

the number of students approximately in Pengrove university = 30,000 or [tex]3 \times 10^4[/tex]

We have to find how many times as much is the number of students at pengrove university as the number of students at Ellentown college.

[tex]\frac{number of students in Pengrove University}{number of students in Ellentown college}[/tex] = [tex]\frac{3 \times 10^4}{3 \times 10^3} = 1 \times 10^1 = 10[/tex]

therefore, 10 times as much is the number of students at pengrove university as the number of students at Ellentown college.

Answer:

-19.322

Step-by-step explanation:

− a + ( − b ) −a+(−b)

First step is to combine like terms

-a -a + -b + -b

-2a -2b

We know a = 6.05 and b = 3.611

-2 (6.05)  -2(3.611)

-12.1 - 7.222

-19.322

Answer:

Step-by-step explanation:-9.661

Answer:

48x² + 96x - 252  

Step-by-step explanation:

    (4x - 6) × 6(2x + 7)    Reorder the factors

= 6(4x – 6)(2x+ 7)          Multiply the binomials

= 6(8x² + 16x - 42)         Remove parentheses

= 48x² + 96x - 252

Answer: You would give your friend 5 cookies

Step-by-step explanation:

One half of the cookies, is basically saying divided by two. 10 divided by 2 is 5. To check that answer, multiply 5 by 2, and you will get 10

Answer:

Step-by-step explanation:

We are given value of tangent trigonometric ratio = 5.6922.

We need to find the angle in degrees whose measure has a tangent of 5.6922..

So, we need to find the value of [tex]tan^{-1}(5.6922)[/tex].

On plugging [tex]tan^{-1}(5.6922)[/tex]in calculator, we get

80.03°.

Now, we need to round it to the nearest whole degree.

Therefore, 80.03°≈ 80°.

Answer to your question:

f(x)= 12x

Answer:

f(x)=12 Hope this helps you!

Answer:

1.  y = 2x-4

2 y = -1/2x+3

Step-by-step explanation:

Slope intercept form of the equation is y= mx+b

where m is the slope and b is the y intercept

1.  y- 2x = -4

We need to solve for y

Add 2x to each side

y -2x+2x = 2x-4

y = 2x-4

2 y-3 = -1/2 x

We need to add 3 to each side

y-3+3 = -1/2x +3

y = -1/2x+3

Answer:

1. y = 2x - 4

y = -1/2x + 3

Step-by-step explanation: You have to isolate or get y by itself.

1:

y - 2x = -4

 + 2x    + 2x

y = 2x - 4

2:

y - 3 = -1/2x

  + 3   + 3

y = -1/2x + 3

Answer:

The answer is 6

Step-by-step explanation:

What you do is this.  

3/9 times 18/1 because you need to make 18 a fraction and then multiply. And you will get 6

Answer:

3

Step-by-step explanation:

Count 1 to 5 (1,2,3,4,5). You can see 3 is between 2 and 4.

A number that comes between 2 and 4 would be 3.

Used the concept of a number system that states,

A writing system used to express numbers is known as a number system. It is the mathematical notation used to consistently express the numbers in a particular set using digits or other symbols.

Given that,

Two numbers are 2 and 4.

Let us assume that the number that comes between 2 and 4 is, x

Then,

[tex]x = \dfrac{(2 + 4)}{2}[/tex]

[tex]x = \dfrac{(6)}{2}[/tex]

[tex]x = 3[/tex]

Therefore, the number would be 3 which comes between 2 and 4.

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Answer:

100/3 or 33.33

Step-by-step explanation: If the perimeter of the whole figure is 220, we can use that number to solve the equations on the trapezoid.

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

4x - 6 + 8 + 8x + 2

12x + 2

Now we have to set the equation equal to the perimeter to find the value of x

12x + 2 = 220

12x = 218

x = 109/6

Since we are only finding the length of PS, we will plug x into its equation (2x - 3).

2(109/6) - 3

109/3 - 3

109/3 - 9/3

100/3

check the picture below.

[tex]\bf \stackrel{\textit{perimeter of the trapezoid}}{(4x+1)+(4x+1)+(4)+(4)+(2x-3)+(2x-3)} \implies 12x+4[/tex]

Answer: C

Step-by-step explanation: A = 10 for one person. B = 7.5 for one person. C = 6.67 for one person. D = 8.75 for one person. E = 10 for one person.

Out of all of these, C is the cheapest.