What is Y=6x-6 and -3x-3y=-24
System of substitution

Answer:How much soy sauce does Bonnie mix with every 1 millimeter of vinegar is 1.5

How much vinegar does bonnie mix with 1 millimeter of soy sauce is .666

Step-by-step explanation: The first is 150 divided by 100 is 1.5

Answer:

The average rate is 35 miles per hour

Step-by-step explanation:

To get from town A to town B takes 3 hours.  The distance is 100 miles

To get from town B to  town c takes 1 hours.  The distance is 40 miles

To find the average rate , we need to find the total distance and divide by the total time

Total distance = 100 + 40 = 140 miles

Total time = 3 hrs + 1 hr = 4 hours

distance = rate * time

140 miles = rate * 4 hours

140/4 = rate

35 = rate

The average rate is 35 miles per hour

Answer:

40x/(15x²y²)

Step-by-step explanation:

    8/(3xy²)       Multiply by 5/5

= 40/(15xy²)     Multiply by x/x

= 40x/(15x²y²)

Answer:

4.66 years

Step-by-step explanation:

Let us assume that it will take 't' years for him to repay the money that he would borrow.

We can use monthly cashflow formula:

[tex]C=Pr\frac{(1+r)^{12t}}{(1+r)^{12t}-1}[/tex]

Here, we have been given:

Monthly cashflow C=425

Loan amount P=20000

Interest rate AMR = 7.5%. Therefore, we have [tex]r=\frac{0.075}{12}[/tex]

Upon substituting these values in the formula, we get:

[tex]425=20000\cdot \frac{0.075}{12} \frac{(1+\frac{0.075}{12})^{12t}}{(1+\frac{0.075}{12})^{12t}-1}[/tex]

Upon simplifying, we get:

[tex]425=125 \frac{(1+0.00625)^{12t}}{(1+0.00625)^{12t}-1}[/tex]

[tex]425=125 \frac{(1.00625)^{12t}}{(1.00625)^{12t}-1}[/tex]

Upon solving this equation using a calculator, we get:

[tex]t=4.66[/tex]

Therefore, correct answer is 4.66 years. That is, second choice from the given options.

Answer:

15.8125 lb

Step-by-step explanation:

Answer:

15 lb. 13oz.

Step-by-step explanation:

no need

Answers: choice A, choice C

Compute the discriminant (use a = 1, b = 5, c = 11)

D = b^2 - 4ac

D = 5^2 - 4*1*11

D = 25 - 44

D = -19

The discriminant is negative, so the two solutions are complex or imaginary. The -19 will be under the root as choice A and choice C show

Answer:

5 : 3

Step-by-step explanation:

the ratio of length : width

= 10 : 6 ← divide both parts of the ratio by 2

= 5 : 3 ← in simplest form

Answer:

i dont know

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

I believe you would take the number of students and divide by the number of members

Answer:

(7)

error percentage is 0.6%

(8)

Graph-C

Step-by-step explanation:

(7)

we are given cube

Let's assume edge of cube =x

so, volume of cube will be

[tex]V(x)=x^3[/tex]

we are given

V=125000

so, we can find 'x'

[tex]125000=x^3[/tex]

[tex]x=50[/tex]

So,

[tex]a=50[/tex]

now, we can use linear approximation formula

[tex]L(x)=V(a)+(x-a)V'(a)[/tex]

[tex]L(x)=V(a)+(\Delta x)V'(a)[/tex]

we have

[tex]\Delta x=0.1[/tex]

we can plug a=50

[tex]L(x)=V(50)+(0.1)V'(50)[/tex]

[tex]V(x)=x^3[/tex]

we can find derivative

[tex]V'(x)=3x^2[/tex]

now, we can plug x=50

[tex]V'(50)=3(50)^2[/tex]

[tex]V'(50)=7500[/tex]

now, we can plug these values

and we get

[tex]L(x)=V(50)+(0.1)\times 7500[/tex]

[tex]L(x)=V(50)+750[/tex]

[tex]L(x)-V(50)=750[/tex]

so, error is

[tex]error=750[/tex]

now, we can find percentage error

Percentage is

[tex]=\frac{750}{125000}\times 100[/tex]

=0.6%

so, error percentage is 0.6%

(8)

we are given

[tex]s(t)=2e^{-1.5t}sin(2\pi t)[/tex]

We will find derivative

To get velocity , we will find derivative

[tex]s'(t)=\frac{d}{dt}\left(2e^{-1.5t}\sin \left(2\pi t\right)\right)[/tex]

we can use product rule

and we get

[tex]s'(t)=-3e^{-1.5t}sin(2\pi t)+4\pi e^{-1.5t} sin(2\pi t)[/tex]

so, we get velocity equation as

[tex]v(t)=-3e^{-1.5t}sin(2\pi t)+4\pi e^{-1.5t} sin(2\pi t)[/tex]

now, we can draw graph

we can see that firstly , we get maxima and then minima

so, our graph would be

graph-C........Answer

Final answer:

To estimate the percentage error in volume, use the tangent line approximation and find the derivative of the volume function. Then divide the change in volume by the actual volume and multiply by 100%.

Explanation:

To estimate the percentage error in volume, we need to find the derivative of the volume function with respect to the length of one edge of the cube. The volume of a cube is given by V = a^3, where a is the length of one edge of the cube. So, the volume function is V = a^3.

Using the tangent line approximation, we can approximate the change in volume as the derivative of the volume function multiplied by the change in length of one edge of the cube. The derivative of the volume function is dV/da = 3a^2. The change in length of one edge is ±0.1 cm. So, the change in volume is approximately dV = (3a^2) * (±0.1 cm).

To find the percentage error in volume, we divide the change in volume by the actual volume and multiply by 100%. The actual volume is 125,000 cm^3. So, the percentage error in volume is approximately [(3a^2) * (±0.1 cm)] / (125,000 cm^3) * 100%.

Answer:

Step-by-step explanation:

Given expression 9+8.

We need to rewrite it using Commutative Property.

Note: According to Commutative Property of Addition

a + b = b + a

Therefore,

We just need to swap the positions of numbers.

Second expression : 91+0

We need to rewrite it using Identity.

According to Identity property of addition

a+0 = a.

When we add 0 to any number it gives same number.

Therefore,

Answer:

C

Step-by-step explanation:

Since GK bisects ∠FGH then ∠FGK = ∠KGH, hence

6v - 2 = 4v + 4 ( subtract 4v from both sides )

2v - 2 = 4 ( add 2 to both sides )

2v = 6 ( divide both sides by 2 )

v = 3 → C

Answer:

Proportion states that the two ratio or fractions are equal.

Given the statement: One grain of sand approximately weighs 7 * 10^{-5} g.

To find how many grains of sand are there in 6300 kg of sand.

Let x be the number of grains of sand in 6300 kg of sand.

Using conversion :

1 kg = 1000 g

6300 kg = 6300000 g

Then, by using proportion method, we have;

[tex]\frac{1}{7\times 10^{-5}}= \frac{x}{6300000}[/tex]

[tex]\frac{10^5}{7} = \frac{x}{6300000}[/tex]

By cross multiply we get;

[tex]6300000 \times 10^5 = 7x[/tex]

or

[tex]63 \times 10^5 \times 10^5 = 7x[/tex]

[tex]63 \times 10^{5+5} = 7x[/tex]  [using [tex]x^a \cdot x^b = x^{a+b}[/tex]]

[tex]63 \times 10^{10} = 7x[/tex]

Divide both sides by 7 we get;

[tex]x = \frac{63 \times 10^{10}}{7} = 9 \times 10^{10}[/tex]

Standard form is a way of of writing down very large or very small numbers easily.

Therefore, [tex]9 \times 10^{10}[/tex] grains of sand are there in 6300 kg of sand.

Answer:

The family formed by these numbers is 3x where x is any integer number.

Step-by-step explanation:

We have been given 3 9 12

We can see that given numbers are multiple of 3 so, we can say that the given numbers are from the family of 3x

Where x is any integer number when multiplied by 3 will give the multiple of 3.

There are many ways to answer this. Here is one answer shown below

AB/WX = BC/XY

On the left side is the ratio of AB over WX. These two sides are the bottom horizontal portions of the triangles. This is a visual indication that they correspond to one another. More concrete proof of this is that AB and WX are the first two letters of the sequences ABC and WXY respectively. The order is very important to help establish pairs like this.

On the right side of that equation above, we have BC and XY as the diagonal sides on the right part of each triangle. They are the last two letters of ABC and WXY respectively, which is a non-visual way to prove these two sides correspond.

It might help to line up ABC over top WXY so you can pick out the corresponding sides. I show this in the attached image below.

Answer: There are many ways to answer this.

Step-by-step explanation:

On the left side is the ratio of AB over WX. These two sides are the bottom horizontal portions of the triangles. This is a visual indication that they correspond to one another. More concrete proof of this is that AB and WX are the first two letters of the sequences ABC and WXY respectively. The order is very important to help establish pairs like this.

On the right side of that equation above, we have BC and XY as the diagonal sides on the right part of each triangle. They are the last two letters of ABC and WXY respectively, which is a non-visual way to prove these two sides correspond.

Answer:

the answer is rectangle

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

For direct variation y=kx, where k is the constant of proportionality

We need to get the equation in this form

3y = 15x

Divide each side by 3

3y/3 =15x/3

y = 5x

The constant is 5

Answer:

y= 1/2 x +11/2

Step-by-step explanation:

To find the slope

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

  = (8-5)/(5--1)

  = 3/(5+1)

  = 3/6

  = 1/2

Using point slope form of a line

y-y1 = m(x-x1)

y-5 = 1/2(x--1)

y-5 = 1/2(x+1)

Distribute

y-5 = 1/2x +1/2

Add 5 to each side

y = 1/2x + 1/2 + 5

Change 5 to 10/2

y = 1/2x + 1/2 + 10/2

y = 1/2x + 11/2

Slope-intercept form:

y = mx + b

"m" is the slope, "b" is the y-intercept (the y value when x = 0) or (0,y)

To find the slope, you can use the slope formula and plug in the two points:

(-1,5) = (x₁ , y₁)

(5,8) = (x₂ , y₂)

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{8-5}{5-(-1)}[/tex]

[tex]m=\frac{8-5}{5+1} =\frac{3}{6} =\frac{1}{2}[/tex]

y = 1/2x + b

To find "b", plug in either of the points into the equation:

(5,8)

y = 1/2x + b

8 = 1/2(5) + b

8 = 5/2 + b      Subtract 5/2 on both sides

8 - 5/2 = b         Make the denominators the same in order to subtract them

16/2 - 5/2 = b

11/2 = b

[tex]y = \frac{1}{2}x+\frac{11}{2}[/tex]    

The 3rd option is your answer

Answer:

2

Step-by-step explanation:

evaluate from left to right, substituting the given values into the expression

= [tex]\frac{70}{10}[/tex] + (5 × 3) - (2 × 10)

= 7 + 15 - 20

= 22 - 20

= 2

Substitute the values of a and b to the expression:

[tex]a=3,\ b=10\\\\\dfrac{70}{b}+5a-2b=\dfrac{70}{10}+(5)(3)-(2)(10)\\\\=7+15-20=22-20=\boxed2[/tex]

Answer:

a = (D+f) * g

Step-by-step explanation:

We want to isolate a

a/g -f =D

Add f to each side

a/g -f+f = D+f

a/g = D+f

Multiply each side by g

a/g *g = (D+f) * g

a = (D+f) * g

[tex]\dfrac{a}{g}-f=D\qquad\text{add f to both sides}\\\\\dfrac{a}{g}=D+f\qquad\text{multiply both sides by }\ g\neq0\\\\\boxed{a=g(D+f)}\qquad\text{use distributive property}\\\\\boxed{a=Dg+fg}[/tex]

Answer: You can get 6 pounds of apples and approximately 19 apples.

Step-by-step explanation:

There are 16 ounces per pound so 6 pounds is 96 ounces

96/5 = 19.2

You can buy 6 pounds of apples for 9, which is approximately 19 apples.

1. First, let's find out how much one pound of apples costs. Since two pounds cost $3.00, one pound would cost half of that, which is $1.50.

2. Now, if one pound costs $1.50, we can find out how many pounds of apples you can buy for $9 by dividing $9 by the cost per pound: [tex]\( \frac{9}{1.50} = 6 \)[/tex]. So, you can buy 6 pounds of apples for $9.

3. Since 1 pound equals 16 ounces, 6 pounds equal [tex]\( 6 \times 16 = 96 \)[/tex]ounces.

4. If one apple is approximately 5 ounces, then the number of apples you can buy for 96 ounces is [tex]\( \frac{96}{5} \).[/tex]

5. Performing the division, [tex]\( \frac{96}{5} = 19.2 \)[/tex]. Since you can't buy a fraction of an apple, you'd round down to the nearest whole number.

6. So, you can buy approximately 19 apples for $9.

Here's the calculation step by step:

1. Cost per pound: [tex]\( \frac{3.00}{2} = 1.50 \)[/tex] dollars per pound.

2. Pounds you can buy for $9: [tex]\( \frac{9}{1.50} = 6 \)[/tex] pounds.

3. Total ounces: [tex]\( 6 \times 16 = 96 \)[/tex] ounces.

4. Apples you can buy: [tex]\( \frac{96}{5} = 19.2 \)[/tex](rounded down to 19 apples).

Answer:

y = -3x+20

Step-by-step explanation:

First we will write the equation in point-slope form,

[tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point on the line.

We must find the slope.  The formula for slope is

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

Using our two points, we have

m = (8-2)/(4-6) = 6/-2 = -3

We will use the first point and this slope:

y-2 = -3(x-6)

Using the distributive property, we have

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

y - 2 = -3x--18

y - 2 = -3x+18

Add 2 to each side:

y-2+2 = -3x+18+2

y = -3x+20

Answer:

g(x) = |x + 3|

Step-by-step explanation:

The x is replaced by x + 3

The equation of g(x) is | x + 3 | when g ( x ) is translated 3 units to the left

How does the transformation of a function happen?

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs)

Horizontal shift (also called phase shift):

Given data ,

The function f(x) = | x | , this function is needed to be translated 3 units to the right. Therefore, the new function can be written as ,

g ( x ) = f ( x + 3 )

     = | x + 3 |

Hence, the equation of g(x) is | x + 3 |.

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[tex]A(n)=5+(n-1)\left(\dfrac{1}{6}\right)=5+\dfrac{1}{6}n-\dfrac{1}{6}=\dfrac{1}{6}n+\dfrac{30}{6}-\dfrac{1}{6}\\\\A(n)=\dfrac{n+29}{3}\\\\\text{Put n = 1, n = 4 and n  = 10 to the formula:}\\\\A(1)=\dfrac{1+29}{3}=\dfrac{30}{3}=10\\\\A(4)=\dfrac{4+29}{3}=\dfrac{33}{3}=11\\\\A(10)=\dfrac{10+29}{3}=\dfrac{39}{3}=13[/tex]

Answer:

{3, 5, 6, 7 }

Step-by-step explanation:

to find the range of f(x) substitute the given values of x from the domain into f(x)

f(- 3) = - (- 3) + 4 = 3 + 4 = 7

f(- 2) = - (- 2) + 4 = 2 + 4 = 6

f(- 1) = - (- 1) + 4 = 1 + 4 = 5

f(1) = - 1 + 4 = 3

range y ∈ {3, 5, 6 , 7 }

Final answer:

The number in question is 70, found by solving the equation 1/2 * x - 25 = 10.

Explanation:

To find a number where half of that number, subtracted by 25, equals 10. We can set up an equation to represent this: 1/2 * x - 25 = 10, where 'x' is the number we are trying to find. To solve for 'x', we first add 25 to both sides of the equation, which gives us 1/2 * x = 35. Then, to isolate 'x', we multiply both sides by 2, resulting in x = 70. Therefore, the number is 70.

Final answer:

To find the number, isolate the variable by performing inverse operations. The number is 70.

Explanation:

To find the number, we need to translate the given information into an equation. Let's assume the number is x. The equation can be written as:

1/2x - 25 = 10.

To isolate the variable x, we first add 25 to both sides of the equation:

1/2x - 25 + 25 = 10 + 25.

This simplifies to 1/2x = 35.

Next, we multiply both sides of the equation by 2 to undo the division by

1/2: 2 × (1/2x) = 2 × 35.

The 1/2 cancels out on the left side, leaving us with x = 70.

Therefore, the number is 70.

Answer:

47 squared units.

Step-by-step explanation:

I'm not sure what you're trying to ask, but if you're trying to find the individual cost;

Solution: Cost of 1 candy bar is $0.91

Explanation: The quotient of 10 and 11 is 0.90909090909, which rounds into 0.91

Hope This Helps!!!

-Austint1414

One chocolate bar costs approximately 0.91 dollars.

Let x be the cost of one chocolate bar.

Given that 11 chocolate bars cost 10 dollars, we set up a proportion:

11 bars / 10 dollars = 1 bar / x dollars

To get cost of one chocolate bar (x), we cross-multiply:

11 * x = 10 * 1

11x = 10

x = 10 / 11

x ≈ 0.91 dollars.

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Full question:

11 chocolate bars cost 10 dollars. How much does 1 chocolate bars cost?

Answer:

3

Step-by-step explanation:

Answer:

30%

Step-by-step explanation:

there is a 60% chance of getting a red marble each time. You need to choose a ball twice. 60/2=30. therefore there is a 30% chance of getting two reds.

Final answer:

To find the probability of drawing two red marbles with replacement from a jar of six red and four blue marbles, we multiply the probability of drawing a red marble (3/5) by itself, resulting in 9/25.

Explanation:

The question asks for the probability that both marbles will be red when two marbles are chosen one at a time with replacement from a jar containing six red marbles and four blue marbles.

To find this, we calculate the probability of drawing a red marble, and since we replace the marble each time, this probability does not change with each draw. With six red marbles out of a total of 10, the probability of drawing a red marble on the first draw is 6/10 or 3/5. Since we replace the marble after each draw, the probability remains the same for the second draw.

Therefore, the probability of drawing two red marbles in a row is (3/5) * (3/5), which is 9/25.