Which first step could you take to solve this system using elimination?
Equation #1: 2x + 18y = -9
Equation #2: 4x + 18y = -27
(Choose all correct answers)
Multiply equation #1 by 2
Multiply either equation by -1
Multiply equation #1 by -2
Multiply equation #1 by -3

Answer: 1.24

Step-by-step explanation:

40% abundance to decimal = 0.4

0.4 multiplied by 3.1 = 1.24

Answer:

1218

Step-by-step explanation:

because when you get to know that it will give you the answer

Answer:

The equation that can be used to determine the average number of miles Keilantra would have to ride each day to meet her goal is:

(28.8 - 4) / 4 = m

This equation subtracts the 4 miles Keilantra has already ridden from her goal of 28.8 miles, and then divides the result by the number of days she still needs to ride (4) to find the average number of miles she would have to ride each day to meet her goal.

Solving this equation gives: (28.8 - 4) / 4 = m

24.8 / 4 = m

6.2 = m

Therefore, the average number of miles Keilantra would have to ride each day to meet her goal is 6.2 miles.

Step-by-step explanation:

Answer:

5.590

Step-by-step explanation:

The quadratic function represented by the table is f(x) = -x² + 4x -1.

A polynomial of degree two in one or more variables is referred to as a quadratic polynomial. The polynomial function that a quadratic polynomial defines is known as a quadratic function.

Here, we have

Given: we have three variables a, b, and c, we can solve this problem by taking three points, say:

(0,-1), (2,3), and (4,-1)

Since we know that the function of the table is a quadratic function, we can start writing this function as follows:

f(x) = ax² + bx + c

So these points must satisfy the equation of the function.

For, (0,-1)

-1 = a(0)² + b(0) + c

c = -1

For, (2,3)

3 = a(2)² + b(2) + c

3 = 4a + 2b -1

4 = 4a + 2b

2 = 2a + b....(1)

For,  (4,-1)

-1 = a(4)² + b(4) + c

-1 = 16a + 4b - 1

4a + b = 0...(2)

Now, we have two equations to solve for a and b:

a = -1

b = 4

Now we put the value of a, b, and c in the given equation and we get

f(x) =  (-1)x² + 4x + (-1)

f(x) = -x² + 4x -1

Hence, the quadratic function represented by the table is f(x) = -x² + 4x -1.

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Answer:

Step-by-step explanation:

Surface area of a triangular prism: The surface area of a triangular prism is given by A=bh+(b1+b2+b3)l units2 A = b h + ( b 1 + b 2 + b 3 ) l units 2 where b is the base of a triangular face, h is the height of a triangular face, b1 , b2 , and b3 are the sides of the triangular base, and l is the length of the prism.

The function will be g(x ) = x² + 2

A function is a special form of relation where each input has exactly one output. In other words, for each input value, the function returns exactly one value. A relation rather than a function is depicted in the above graph since one is mapped to two different values.

But, if one were instead mapped to a single value, the relationship described above would change into a function. Furthermore, output values could match input values exactly.

The function machine receives the x-values as input. After finishing its operations, the function machine produces the y-values. Any function may be the one within.

g(x) = x2 + 2

Now we need to but this in vertex form.

If you graph this equation, you will see that the vertex is (0,2). Plug this in to (h,k) in the equation. The value of a is just 1 because you didn't multiply by anything during the transformation.

So you get g(x) = (x-0)2 + 2 = x2 + 2

This ends up just being the same as the standard form of the equation

Hence, The function will be g(x ) = x² + 2

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The value of cot A is √55/3

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

cot A = 1/tanA

AC = √ 8²-3²

AC = √64-9

AC = √ 55

tanA = 3/√55

cot A = 1/tanA

cot(A )= 1/(3/√55)

cot( A) = √55/3

therefore the value of cot(A) = √55/3

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The value of x and y in the triangle are 0 and 4 respectively.

The mid segment of a triangle is a line connecting the midpoints between two sides of a triangle. The mid segment theorem states that the midsegment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle, and the length of this midsegment is half the length of the third side .

Therefore,

x + 2 = 3 / 2 x + 2

x - 3 / 2 x = 2 - 2

-0.5x = 0

x = 0

Let's find y

2y - 1 = 3y - 5

2y - 3y = -5 + 1

-y = -4

y = 4

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The value of the variables are as follows:

The value of the variables is given as follows:

sin 45° = 39/z

z = 39/sin 45°

sin 45° = 1/√2

z = 39 / 1/√2

z = 39√2

Let the height of the triangle be h;

cos 45 = h/39√2

cos 45 = 1/√2

h = 39√2 * 1/√2

h = 39

tan 60° = 39/y

tan 60° = √3

y = 39/√3

y = 13√3

sin 60° = 39/x

x = 39 / sin 60°

sin 60° = √3/2

x = 39 /√3/2

x = 26√3

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Answer: 6 cups of flour = 4 cups of sugar

              9 cups of flour = 6 cups of sugar

             12 cups of flour = 9 cups of sugar

Step-by-step explanation:

Well, if Kurt uses 3 cups of flour for every 2 cups of sugar, than for every 6 cups of flour, he would need 4 cups of sugar. With 9 cups of flour, he would need 6 cups of sugar. For 12 cups of flour, he would need 9 cups of sugar.

Answer:yes

Step-by-step explanation:

Answer:

We can start the problem by using the formula for the area of a rectangle:

Area = length x width

The total area of the pool and the walkway is given as 360 square feet. Let's assume that the width of the walkway is w feet. Then, the dimensions of the entire area can be represented as (8 + 2w) by (10 + 2w) feet, since there is an additional width of w feet on both sides of the pool. Therefore, we can set up the equation:

(8 + 2w) x (10 + 2w) = 360

Expanding the left side and simplifying, we get:

4w^2 + 36w - 80 = 0

We can solve for w using the quadratic formula:

w = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 4, b = 36, and c = -80. Substituting these values into the formula, we get:

w = (-36 ± sqrt(36^2 - 4(4)(-80))) / 8

w = (-36 ± sqrt(1872)) / 8

w ≈ -5.6 or w ≈ 3.6

Since the width cannot be negative, we can discard the first solution. Therefore, the width of the walkway should be approximately 3.6 feet.

Step-by-step explanation:

Answer:

We can start the problem by using the formula for the area of a rectangle:Area = length x widthThe total area of the pool and the walkway is given as 360 square feet. Let's assume that the width of the walkway is w feet. Then, the dimensions of the entire area can be represented as (8 + 2w) by (10 + 2w) feet, since there is an additional width of w feet on both sides of the pool. Therefore, we can set up the equation:(8 + 2w) x (10 + 2w) = 360 Expanding the left side and simplifying, we get:4w^2 + 36w - 80 = 0We can solve for w using the quadratic formula:w = (-b ± sqrt(b^2 - 4ac)) / 2aIn this case, a = 4, b = 36, and c = -80. Substituting these values into the formula, we get:w = (-36 ± sqrt(36^2 - 4(4)(-80))) / 8w = (-36 ± sqrt(1872)) / 8w ≈ -5.6 or w ≈ 3.6Since the width cannot be negative, we can discard the first solution. Therefore, the width of the walkway should be approximately 3.6 feet.

Step-by-step explanation:

Using trigonometric identity,  the exact value of sin(A + B) in simplest radical form is 17√5 / 25√13.

We can use the trigonometric identity for the sine of the sum of two angles:

sin(A + B) = sin(A)cos(B) + cos(A)sin(B)

We know that Tan A = 8 and that angle A is in quadrant 1. We can use the fact that Tan A = sin(A)/cos(A) to find sin(A) and cos(A)

[tex]Tan A = sin(A)/cos(A)\\sin(A) = Tan A * cos(A) = 8 * (1 / \sqrt(1 + Tan^2 A)) = 8 / \sqrt(65)\\cos(A) = 1 / \sqrt(1 + Tan^2 A) = 1 / \sqrt(65)[/tex]

We also know that sin B = 1/sqrt(5). Since angle B is in quadrant 1, we can use the Pythagorean identity cos^2(B) + sin^2(B) = 1 to find cos(B):

[tex]cos(B) = \sqrt(1 - sin^2(B)) = \sqrt(1 - 1/5) = 2\sqrt(5) / 5[/tex]

Now we can substitute these values into the formula for sin(A + B):

sin(A + B) = sin(A)cos(B) + cos(A)sin(B)

[tex](8 / \sqrt(65)) * (2\sqrt(5) / 5) + (1 / \sqrt(65)) * (1 / \sqrt(5)) = (16\sqrt(5) + 1) / (5\sqrt(325))[/tex]

We can simplify this fraction by multiplying the numerator and denominator by √5:

[tex]sin(A + B) = ((16\sqrt(5) + 1) / (5\sqrt(325))) * (\sqrt(5) / sqrt(5))\\ = (16\sqrt(5) + \sqrt(5)) / (25\sqrt(13))\\ = (17\sqrt(5)) / (25\sqrt(13))[/tex]

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Answer:

A. 0.34

Step-by-step explanation:

  1.7

x 0.2

_____

   .14

+ .20

______

.34

Answer:

[tex]4992 \text{ cm}^2[/tex]

Step-by-step explanation:

We can model the amount of metal, in square centimeters, that is needed to make a soup can with the expression:

[tex](2 \cdot \text{area of base}) + (\text{area of side})[/tex]

We can first solve for the surface area of a soup can, using the fact that its bases are circles.

[tex]A_{\text{circle}} = \pi r^2[/tex]

↓ substituting 3 for π

[tex]A_{\text{base}} = 3r^2[/tex]

↓ plugging in radius (which is 1/2 of diameter, given as 8)

[tex]A_{\text{base}} = 3(4)^2[/tex]

↓ simplifying

[tex]A_{\text{base}} = 48 \text{ cm}^2[/tex]

Then, we can solve for the area of its side, which we can think of as an elongated circumference (circumference multiplied by height).

[tex]A_{\text{circumference}} = \pi d[/tex]

[tex]A_{\text{side}} = h(\pi d)[/tex]

↓ substituting 3 for π

[tex]A_{\text{side}} = h(3d)[/tex]

↓ plugging in height and diameter

[tex]A_{\text{side}} = 9(3 \cdot 8)[/tex]

↓ simplifying

[tex]A_{\text{side}} = 216 \text{ cm}^2[/tex]

Next, we can solve for the surface area of one soup can.

[tex](2 \cdot \text{area of base}) + (\text{area of side})[/tex]

↓ plugging in solved values

[tex](2 \cdot 48 \text{ cm}^2) + 216 \text{ cm}^2[/tex]

↓ simplifying

[tex]96 \text{ cm}^2 + 216 \text{ cm}^2[/tex]

↓ performing addition

[tex]312 \text{ cm}^2[/tex]

Finally, we can solve for the amount of metal needed for 16 cans by multiplying the amount for 1 can by 16.

[tex]16 \cdot 312 \text{ cm}^2[/tex]

↓ performing multiplication

[tex]\boxed{4992 \text{ cm}^2}[/tex]

First three sum 1/10 + 2/10 + 4/10 Proof: When the numbers in the denominator have the same value, fractions can be compute only with the sum of numerator values and the denominator doesn’t change. 1/10 + 2/10 + 4/10 = 1+2+4 / 10 = 7/10 Second three sum 1/10+1/5 + 2/5, Proof: such kind of fractions can be computed as follows: 1/10 + (1+2 )/5 (same denominators). 1/10 + (1+2 )/5= 1/10 + 3/5= 5x1 +10x3 / 5x10 = 5+30 /50 =35/50, by simplifying by 5, 35/50=7/10 The third three sum is 5/10+ 3/15+8/20,it can be computed by using the same method as given above

Hope it helps

Option A is correct, 162 is the greatest number of caps she can buy.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

Let x be the number of caps.

We have been given that cost of one cap is $6, so cost of x caps will be equal to 6x.

We are also told that the company charges an amount of $25 for shipping, so total cost of buying x caps will be equal to the cost of x caps plus shipping charges (6x+25).

Since Laura has a budget of $1,000, so cost of x caps will be less than or equal to 1,000.

We can represent this information in an equation as:

6x+25≤1000

Let us solve for x

Subtract 25 from both sides

6x≤1000-25

6x≤975

Divide both sides by 6

x≤162.5

Hence, Option A is correct, 162 is the greatest number of caps she can buy.

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The surface area of the shape when a cube is taken out of it would be = 164.

The surface area is defined as the area that is being occupied by outer surface of a shape of object.

The surface area of a given shape = 314

An area of a cube shape is taken out of it with sides = 5×5

The area of a cube = 6(a²)

where a = 5

area of the cube = 6(5²)

= 6×25 = 150

Therefore, the surface area of the shape after area of cube such as = 150 has been removed from it ;

= 314-150

= 164.

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Answer:

25

Step-by-step explanation:

let the no of days food avl for eat be X .

according to question...

100/80=X/20

=X × 80 = 100×20

=80x =2000

= x =2000/80

x=25 days

Therefore, the percentage increase in the price of petrol is approximately 5.57%.

One tenth of any amount is represented by the relative number 10% in the image. Since one percent (1%) represents the one tenth of something, 100 percent (100%) denotes the entire thing, and 200 percent (200%) denotes twice the amount indicated. percentage. Mathematical percentile is a similar subject.

To find the percentage increase in the price of petrol, we can use the formula:

percentage increase = (new value - old value) / old value x 100%

Here, the old value is R12.58 per litre, and the new value is R13.28 per litre. Substituting these values into the formula, we get:

percentage increase = (13.28 - 12.58) / 12.58 x 100%

percentage increase = 0.70 / 12.58 x 100%

percentage increase = 0.0557 x 100%

percentage increase = 5.57%

Therefore, the percentage increase in the price of petrol is approximately 5.57%.

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Answer:

I do not have access to drawing tools to create a graph. However, I can explain how to plot the function h on the graph based on the given information.

The function h(x) has two parts:

For x < -3, the value of h(x) is J-4.

For x >= -3, the value of h(x) is x-3.

To plot this on a graph, you would need to draw a vertical line at x = -3 to separate the two parts of the function. Then, for x < -3, you would plot a horizontal line at a height of J-4 to represent the constant value of h(x) in that region. For x >= -3, you would plot the line y = x-3.

I hope this explanation helps you to plot the function h on the graph!

Step-by-step explanation:

Answer:

See Picture

Step-by-step explanation:

The original sin(x) function starts at (0,0) and oscillates around the x-axis between y=1 and y=-1, intercepting it in intervals of π.

To graph sin(x)-2 then, we simply need to graph a sin(x) function 2 units lower.

In linear equation, Tammy will have made a profit of $103,768.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                    Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

Let x be the number of years after Tammy purchased her home.

We have been given that Tammy’s home cost her $184,000. She lives in an area with a lively real estate market, and her home increases in value by 3.5% every year.

We can see that value of house will increase exponentially as the value of increases 3.5% per year.

Since an exponential function is in form

           y = a * bˣ

a = Initial value,

b = For growth b is in form (1+r) where r represents growth rate in decimal form.

Let us convert our given growth rate in decimal form.

   3.5% = 0.035

Upon substituting our values in exponential form of function we will get the value (y) of Tammy's home after x years as

  y = 184000(1 + 0.035)ˣ

 y =  184000(1.035)ˣ

  Therefore, the function   y =  184000(1.035)ˣ represents value of Tammy's home after x years of purchase.

Let us find the value of home after 13 years by substituting x=13 in our function.

     y =  184000(1.035)¹³

     y =  184000 * 1.56395606

  y = 287767.915

  Let us subtract cost of the home from the value of home after 13 years to find the amount of profit.

   The amount of profit, if tammy sells her home after 13 years = 287767.915  - 184000  

 The amount of profit, if tammy sells her home after 13 years = 103767.915 - 103,768

Therefore, Tammy will have made a profit of $103,768.

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The maximum and minimum of the given function are 22 and -2, respectively

The system of inequalities is given as

y ≥ -x - 2

y ≥ 3x + 2

y ≤ x + 4

See attachment for the graph

From the graph, we have the following coordinates

(-1, -1), (-3, 1) and (1, 5)

Substitute (-1, -1), (-3, 1) and (1, 5) in f(x, y) = -3x + 5y

So, we have

f(-1, -1) = -3(-1) + 5(-1) = -2

f(-3, 1) = -3(-3) + 5(1) = 14

f(1, 5) = -3(1) + 5(5) = 22

Hence, the maximum is 22 and the minimum is -2

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Answer:

Since the ratio of apples to the total pieces of fruit sold is 3/5, we know that the apples section of the graph represents 3/5 of the total angle of the circle graph.

The total angle of a circle is 360 degrees, so we can set up the equation:

3/5 x 360 = angle measure of the apples section

Simplifying the left side, we get:

216 = angle measure of the apples section

Therefore, the angle measure of the apples section of the graph is 216 degrees.

There are 3.79 litres in 4 quarts.

Unit conversion is the conversion between different units and measurements of the same quantity through a process of multiplication or division. In mathematics, conversion is the process of changing values ​​in one form to another form like Inches to millimeters or liters to gallons.

Given in the table

1 quart = 0.9464 liter

4 quarts = 4 × 0.9464 litre

4 quarts = 3.7856 litres

hundredths means 2 digit right to the decimal point

3.7856 litres rounded to nearest hundredths

= 3.79 litres

Hence, 3.79 litres are there in 4 quarts.

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An equation that represents this problem "Anthony read 5/6 hour each day for 2 days." is: A. 2 × 5/6 = 10/12.

In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).

Based on the information provided above, we can reasonably infer and logically deduce that Anthony's reading rate is 5/6 hour on a daily basis and for a period of 2 days only:

Total number of hours = 2 × 5/6

Total number of hours = 10/12 hours.

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Answer:

I'm assuming the question is how many miles in total did mary swim.

if this is the case then we just multiply the number of days by the number of miles per day.

Hence,

3/4 × 8 = 6

so 6 miles in total.

make sure to ask if you need any further help

Step-by-step explanation: