11. Match each step to show how to solve the system of equations using substitution. 7x-2y=-1 x = 6y + 1
Step 1. ____
Step 2. ____
Step 3. ____
Step 4. ____
A-Since the second equation is solved for x, substitute 6y + 1 for x in the first equation. B-Substitute the value for y into either equation to find x.
C-Solve the resulting equation for y.D Write the solution as an ordered pair, and check the solution.
D-write the solution as an ordered pair, and check the solution.​

Answer:

There are 36 possible outcomes when two dice are rolled (6 outcomes for the first die and 6 outcomes for the second die). To find the probability that the sum of the two numbers on the dice will be greater than 9, we need to count the number of outcomes where the sum is greater than 9.

The possible outcomes where the sum is greater than 9 are (4,6), (5,5), (5,6), and (6,5), for a total of 4 outcomes. Therefore, the probability of getting a sum greater than 9 is 4/36 or 1/9.

Answer: C) 1/12.

The equation of the line of best fit for the set of data is given as follows:

y = 4.24773x - 0.32726

To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.

From the table in this problem, the points are given as follows:

(0.9, 3.51), (1.7, 6.61), (3, 12.27), (0.1, 0.15), (2.3, 9.59), (1.3, 5.35), (0.5, 1.65), (2.1, 8.8).

Inserting these points into a calculator, the line of best fit is given as follows:

y = 4.24773x - 0.32726

More can be learned about linear regression at https://brainly.com/question/29613968

#SPJ1

Using the given information, the cost of Max's electricity bill is R551.10

From the question, we are to calculate the cost of Max's monthly electricity bill

From the given information,

"Max's monthly electricity budget only allows him to use 250.50 kWh"

and

"The cost for 1 kWh is R2.20"

To determine the cost of Max's monthly electricity bill, we will multiply his monthly electricity budget by the cost for 1 KWh

That is,

Max's monthly electricity bill = 250.50 × R2.20

Max's monthly electricity bill = R551.10

Hence,

The cost of Max's monthly electricity bill is R551.10

Learn more on Calculating the cost of electricity bill here: https://brainly.com/question/11788281

#SPJ1

To find the percentage of Farmer Gibson's herd that remains after he sold 60 cows, we need to calculate the new total number of cows he has.

Number of cows remaining = Total number of cows - Number of cows sold

Number of cows remaining = 200 - 60

Number of cows remaining = 140

So, Farmer Gibson has 140 cows remaining in his herd.

To find the percentage of cows remaining, we can use the following formula:

Percentage = (Number remaining ÷ Total number) x 100

Plugging in the values we have:

Percentage = (140 ÷ 200) x 100

Percentage = 0.7 x 100

Percentage = 70%

Therefore, Farmer Gibson has 70% of his herd remaining after selling 60 cows.

~~~Harsha~~~

For an increase of one hour in time worked, the predicted increase in the amount of money spent on entertainment will be; 1.86 units.

To Determine the predicted increase in the amount of money spent on entertainment for an increase of one hour in time worked, we need to find the slope of the line, which is the coefficient of x in the equation.

We are given that the equation of the line of best fit, y = −0.76x8.76

The slope is 1.86, that means that for every one unit increase in x (which in this case is one hour worked), y (in this case is the amount of money spent on entertainment) is predicted to increase by 1.86 units.

This is the change in the dependent variable (y) for a unit increase in the independent variable (x),

Based on the linear relationship described by the equation of the line fit.

Learn more about Expression

brainly.com/question/16804733

#SPJ11

Answer:

2(x + 5) = 3(x - 4)

2x + 10 = 3x - 12

x = 22

Result:

Yes, the fifth-grade team will need to ship the order of 325 shirts for Field Day. They will need to package them in 16 boxes to ship them.

To evaluate the number of boxes needed to ship the order, we need to divide the total number of shirts by the number of shirts that can fit in one box.

where:

Number of shirts per box = 21

Total number of shirts = 325

Number of boxes needed = Total number of shirts / Number of shirts per box

Number of boxes needed = 325 / 21

Number of boxes needed = 15.47619

Since we cannot have a fraction of a box, we would round up to the nearest whole number.

Therefore, the fifth-grade team will need to ship the order in 16 boxes.

Learn more about a fraction at brainly.com/question/28699958

#SPJ1

Answer:

x = 27°

Step-by-step explanation:

using the co-function identity

cos x = sin(90 - x) , then

cos63° = sin(90 - 63)° = sin27° with x = 27°

Answer:

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

Based on the tangent line and the radii, the value of x given that AB is tangent to the circle is 10

From the question, we have the following parameters that can be used in our computation:

AB is tangent to the circle

As a general rule:

The radius of circle is perpendicular to the tangent line

This means that we can calculate x using the Pythagorean theorem

So, we have

x^2 = 6^2 + 8^2

Evaluate the sum of exponents

So, we have

x^2 = 100

So, we have

x = 10

Hence, the calculated value of x in the circle is 10

Read more about tangent lines at

https://brainly.com/question/16038958

#SPJ1

Answer:

36cm

Step-by-step explanation:

The lightning bolt on the right is 3 times bigger than the one on the left. You can tell this because that leftside, vertical-ish piece (on both of them) is labelled. The small one is 25cm and the big one is 75cm.

25 × 3 = 75

The bottom right side is 12cm, so times by 3 to find the bigger one that matches.

12 × 3 = 36

Answer:

1/3

Step-by-step explanation:

p(event) = (number of desired outcomes)/(total number of outcomes)

total number of outcomes = 13 + 15 + 17 = 45

number of desired outcomes = 15

p(can of tomato soup) = 15/45 = 1/3

The smallest positive integer a that satisfies the conditions of the problem is a = 2.

The Intermediate Value Theorem states that if a function f(x) is continuous on the interval [a, b] and takes on values f(a) and f(b) at the endpoints a and b, respectively, then for any value c between f(a) and f(b), there exists at least one value x in the interval [a, b] such that f(x) = c.

In this problem, we are asked to find the smallest positive integer a such that the Intermediate Value Theorem guarantees a zero exists between 0 and a for the polynomial f(x) = 3x³ - 4x² - 3x - 1.

To find this value of a, we need to evaluate f(0) and f(a) and look for a value of a such that f(0) and f(a) have opposite signs. This will guarantee the existence of a root of f(x) between 0 and a.

Evaluating f(0), we get:

f(0) = 3(0)³ - 4(0)² - 3(0) - 1 = -1

To find f(a), we need to solve for a using the equation f(a) = 0. We can use a numerical method, such as the Newton-Raphson method or the bisection method, to find the root of f(x) = 0. Using a calculator or a computer program, we find that f(a) = 0 for a ≈ 1.353.

Since f(0) = -1 and f(a) = 0 have opposite signs, the Intermediate Value Theorem guarantees the existence of at least one zero of f(x) between 0 and a = 1.353. Therefore, the smallest positive integer a that satisfies the conditions of the problem is a = 2.

To learn more about polynomial click on,

https://brainly.com/question/23006670

#SPJ1

The distance between Alberto and the base of the building is  93.4ft

We can view this as a right triangle, such that one cathetus (opposite to the known angle) measures:

40ft - 6ft = 34ft

And the known angle is 70°, we want to get the other leg of the right triangle, so we can use the tangent trigonometric relation which is:

tan(angle) = (opposite cathetus)/(adjacent cathetus)

Replacing the things that we know we get:

tan(70) = x/34ft

tan(70)*34ft = x = 93.4ft

That is the distance.

Learn more about right triangles at:

https://brainly.com/question/2217700

#SPJ1

The missing height of the triangle is h = 66 inches

Given data ,

Let's denote the missing height of the triangle as "h" inches.

The formula for the area of a triangle is given by:

Area = (1/2) * base * height

Given that the area of the triangle is 6,460 inches squared and the base is either 136 inches or 196 inches, we can set up two equations to solve for "h".

For the base of 136 inches:

Area = (1/2) * 136 * h

6460 = 68h

h = 6460 / 68

h ≈ 95 inches

For the base of 196 inches:

Area = (1/2) * 196 * h

6460 = 98h

h = 6460 / 98

h ≈ 66 inches

Hence , the height of the triangle is h = 66 inches or 95 inches

To learn more about triangles click :

https://brainly.com/question/16739377

#SPJ1

The value of x is given as follows:

x = 2.5 cm.

Similar triangles are triangles that share these two features listed as follows:

The logic for similar triangles can be expanded for any similar polygons, as is the case for this problem.

The proportional relationship for the side lengths is given as follows:

x/5 = 4/8

Applying cross multiplication, the value of x is obtained as follows:

8x = 20

x = 2.5 cm.

More can be learned about similar triangles at brainly.com/question/14285697

#SPJ1

Four seconds after the boulder is hurled, it will hit the ground.

When the boulder hits the ground, its height will be 0. So, we need to solve the equation:

[tex]h(t) = -16t^2 + 64t = 0[/tex]

We can factor out -16t from the expression:

h(t) = -16t(t - 4)

Setting each factor to zero, we get:

-16t = 0 or t - 4 = 0

Solving for t, we get:

t = 0 or t = 4

Since t = 0 represents the time when the boulder is launched, we can ignore it. Therefore, the boulder will hit the ground 4 seconds after it is launched.

Learn more about function here:

https://brainly.com/question/29633660

#SPJ1

The probability that the sum would be an even number, can be found to be 1 / 2 .

There are six sides on each die so the total number of outcomes is:

= 6 x 6

= 36 outcomes

We will get an even number if we get two odd numbers, and two even numbers. We will not get even, with an even number and an odd number.

The number of two odd number outcomes is:

= 3 x 3

= 9 outcomes

The two even outcomes:

= 3 x 3

= 9 outcomes

The probability that the sum is even is:

= ( 9 + 9 ) / 36 total outcomes

= 18 / 36

= 1 / 2

Find out more on probability at https://brainly.com/question/16932886

#SPJ1

Answer:  the best answer is option A: the data is symmetric with an approximate range of 20. The lowest value of 6 might mean that most students did not participate in activities.

Step-by-step explanation: From the line plot, we can see that the data is not symmetric because the dots are not equally distributed on both sides of the plot. Therefore, we can eliminate options A and C.

Option D suggests that the data is bimodal, meaning that there are two peaks in the distribution. However, there is no clear indication of two peaks in the plot. Therefore, we can eliminate option D.

Option B suggests that the data is skewed, and the most frequent number of activities is 16 or more. However, this is not the case as the highest number of dots is above 14 and 16. Therefore, we can eliminate option B.

The area of the triangle is; 33 in².

The area of the rectangle is; 190 in².

The total area as required is; 223 in².

By observation; the triangle is such that its base is 6 in and it's height is; (20 - 9) = 11 in.

Therefore, the area of the triangle given by; (1/2)×b×h is; (1/2) × 6 × 11 = 33 in².

The area of the rectangle of length 20 in and width 9.5 in is; 20 × 9.5 = 190 in².

Ultimately, the total area of the composite shape is; 33 + 190 = 220 in².

Read more on area of plane shapes;

https://brainly.com/question/4895332

#SPJ1

The population mean is calculated as the sum of all observations in the population, divided by the number of objects in the population.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

Hence the population mean is calculated as the sum of all observations in the population, divided by the number of objects in the population.

The problem is incomplete, hence the procedure to obtain the mean of a data-set, in this case the population, is presented.

More can be learned about the mean of a data-set at https://brainly.com/question/1136789

#SPJ1

Answer: the real zero of this equation is 5/3.

Answer:

45

Step-by-step explanation:

The pair of equivalent expressions that represent the sale price for any one item is  0.75m and m-1/4m. Option C

The sale price of an item is the regular price minus 1/4 of the regular price. This can be represented as:

sale price = regular price - (1/4)regular price

Simplifying this expression, we get:

sale price = (3/4)regular price

Therefore, the sale price for any one item can be represented as 0.75m, which is equivalent to option C.

learn more about equivalent at https://brainly.com/question/15775046

#SPJ1

For 6 servings, the recipe will need 12 cups of sauce and 3/4 teaspoon of oregano. So, the answer is option A: The recipe will need 12 cups of sauce and three-fourths teaspoons of oregano for 8 servings.

To find how much sauce and oregano will be needed to make 6 servings, we can use the ratio of sauce to oregano in the recipe.

For 4 servings, the recipe calls for 8 cups of sauce and 1/2 teaspoon of oregano. To find how much sauce and oregano are needed for 6 servings, we can set up a proportion:

sauce : oregano = 8 cups : 1/2 teaspoon = 16 cups : 1 teaspoon

So, for 6 servings, we need:

sauce : oregano = 16 cups : 1 teaspoon

To convert this to cups and tablespoons, we can multiply both sides of the proportion by 3/4:

sauce : oregano = (16 x 3/4) cups : (1 x 3/4) teaspoons

sauce : oregano = 12 cups : 3/4 teaspoon

sauce : oregano = 48 cups : 3 teaspoons

Therefore, for 6 servings, the recipe will need 12 cups of sauce and 3/4 teaspoon of oregano. So, the answer is option A: The recipe will need 12 cups of sauce and three-fourths teaspoons of oregano for 8 servings.

To know more about ratios and proportions follow

https://brainly.com/question/30073411

#SPJ1

Answer:

3y+8x

Step-by-step explanation:

To solve this problem we first have to add similar terms

Adding like terms:

So let us add up the sides that have the same variable. Let us solve for the variable y first ->

[tex]4+y+2y-2\\\\(y+2y)+(4-2)\\\\3y+2[/tex]

Now we have the simplified form of the y. Now let us solve for x ->

[tex]6x+2+2x-4\\\\(6x + 2x) + (2 - 4)\\\\8x - 2[/tex]

Combine both expressions:

To combine these expressions we add the constants and leave the variables. (We do this because different variables cannot be added together)

[tex]8x - 2 +3y +2\\\\8x + 3y + (-2 + 2)\\\\8x+3y+0\\\\8x+3y[/tex]

So 3y + 8x is the asnwer

Answer:

1) Let x be the distance from Alberto to the base of the building. Using trigonometry, we have:

tan(70) = 40 / (x + 6)

x + 6 = 40 / tan(70)

x = 40 / tan(70) - 6

x ≈ 11.1 feet

Therefore, Alberto is about 11.1 feet away from the base of the building.

2) Let h be the height of the building. Using trigonometry, we have:

tan(θ) = h / (100 + 1.55)

h = (100 + 1.55) tan(23)

h ≈ 42.9 feet

Therefore, the height of the building is about 42.9 feet.

3)  Let θ be the angle of elevation for each ramp. Using trigonometry, we have:

sin(θ) = 22 / 122

θ = sin⁻¹(22/122)

θ ≈ 10.3 degrees

Therefore, the measure of the angle of elevation for each ramp is about 10.3 degrees.

4) Let d be the distance from the boat to the base of the lighthouse. Using trigonometry, we have:

tan(28) = 40 / d

d = 40 / tan(28)

d ≈ 78.5 feet

Therefore, the distance from the base of the lighthouse to the boat is about 78.5 feet.

5) Let x be the distance from General Han Xin's position to the palace. Using trigonometry, we have:

tan(35) = x / 800

x = 800 tan(35)

x ≈ 595.4 meters

Therefore, the palace is about 595.4 meters away from General Han Xin's position.

6) Let h be the height of the clouds. Using trigonometry, we have:

tan(80) = h / 165

h = 165 tan(80)

h ≈ 702.4 meters

Therefore, the clouds are about 702.4 meters high.

Step-by-step explanation:

The area and the circumference of the circle is 1074.6 m² and 116.18 m respectively.

Given that a circle has a diameter of 37 m, we will find the circumference of and the area of the circle,

Radius = diameter /2

Radius = 18.5 m

Circumference = π × diameter

= 3.14 × 37

= 116.18 m

Area = π × radius²

= 3.14 × 18.5²

= 1074.6 m²

Hence, the area and the circumference of the circle is 1074.6 m² and 116.18 m respectively.

Learn more about circle, click;

https://brainly.com/question/29142813

#SPJ1

The data can be stored on the entire reel is 66,355,200 bits.

Conversion could appear difficult, but this tip will make it simple for you to convert any unit. The fundamental rule is to multiply when converting from a larger unit to a smaller unit. Divide if you need to go from a smaller to a larger unit.

We have,

The 6-inch segment of tape stores 4608 bits of data.

Now, length of of reel = 1200 feet

= 1200 x 12

= 14,400 inch

So, the data that can be stored in reel

= 14,400 x 4608

= 66,355,200 bits

Learn more about Unit conversion here:

https://brainly.com/question/19420601

#SPJ2