Graph the line... running through: (1,3) with m=3

To solve this problem we will need a system of equations.

Step 1. Find the first equation.

Using the statement "Emma rented a bike for 4 hours and paid £18", we will call the cost per hour h, and the flat fee f. Thus, the first equation is:

This is because Emma rented the bike for 4 hours but she had to pay a flat fee f, and the total was £18.

Step 2. Find the second equation.

We do the same but now with the statement "Louise rented a bike for 7 hours and paid £25.5". Remember that for our equation, h represents the cost per hour and f the flat fee. The second equation is:

Step 3. In summary, our system of equations is:

Step 4. To solve part a. we have to find the cost per hour "h".

To find it, we use the elimination method in our system of equations, which consists of adding or subtracting the equations in order to eliminate one variable.

Since we are interested in finding "h", we can subtract the second equation from the first one, and we get the following:

Applying the subtraction:

And we start subtracting 7h-4h, which results in 3h:

The next subtraction is f-f, which results in 0.

And then, subtract 25.5-18:

The equation we have as a result is:

Which is an equation we can use to solve for the cost per hour h.

Dividing both sides by 3:

The cost per hour is £2.5

Step 5. To find part b we need to find the rental feed, in our case, this means to find "h".

Using the first equation of the system:

And substituting the previous result:

We get:

Solving the operations:

And solving for f:

the flat fee is £8.

Step 6. To find part c, we consider the cost per hour and the flat fee.

Michael rented the bike for 2 hours.

Since the cost per hour is £2.5, and the flat fee is £8, he will pay:

Solving these operations:

It will cost £13.

Answer:

a. £2.5

b. £8

c. £13

Given that a sugar sweet company costs to transport its sugar, 7500 to rent truck and additional 225 for each ton.

The average number of persons admitted in one year is X/5.

What is average number?

Average By adding a collection of numbers, dividing by their count, and then summing the results, the arithmetic mean is determined.

If X persons are admitted in last 5 years in a hospital.

Then we get the average value of admitted persons are X/5 per year.

If Y persons are recovered in last 5 years in a hospital.

Then we get the average value of recovered persons are Y/5 per year.

Therefore, the average number of persons admitted in one year is X/5.

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The number of pennies they lose altogether is 288 pennies.

Together, Katya and Mimi have 480 pennies in their piggy banks.

Therefore, there total amount of pennies is 480.

After Katya loses 1/2 of her pennies and Mimi loses 2/3 of her pennies, they have an equal number of pennies left.

Therefore,

let

x = number of pennies Katya have

y = number of pennies Mimi have

Hence,

x + y = 480

x = 480

Katya pennies left = x - 1 / 2x = 1 / 2x

Mimi pennies left = y - 2 / 3 y = 1 / 3 y

1 / 2 x  = 1 / 3 y

2y = 3x

y = 3  / 2 x

Substitute the value in equation(i)

x + 3 / 2 x  = 480

2.5x = 480

x = 480 / 2.5

x = 192

Therefore,

192 + y = 480

y = 480 - 192

y = 288

The number of pennies they loose can be calculated as follows;

Therefore, they lost 96 + 192 = 288 pennies altogether.

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Question:

There are 9.75 ounces of Cinnamon Toast Crunch in a bowl. Additional cereal is poured into the bowl at a rate of 1.5 ounces per second. How many ounces are in the bowl after 3 seconds?

Solution:

If additional cereal is poured into the bowl at a rate of 1.5 ounces per second, then in 3 seconds the additional cereal into the bowl is 1.5x 3 = 4.5 ounces. Thus after 3 seconds, the bowl has the original amount that it already had and the new aggregate:

9.75 ounces + 4.5 ounces = 14.25

then, the correct answer is:

14.25

Give the radius of a circle, r, we can find its area by using:

In the picture, the 30 ft segment passes from on side of the circle to the other passing thourhg tht center, so it is the diameter. The radius is half the diameter, so:

Now, we can use the formula for the area to find it:

So, the area is approximately 706.9 ft².

y = 0.34x - 0.9 (Option A)

We are given the data and we want to find the line of best fit.

The line of best fit is a line that goes through the data points and it gives the best representation of the spread of the data.

The equation of a line is given as:

y = mx + c

y represents y-values

x represents x-values

m is the slope of the line

c is the y-intercept of the line or where the line crosses the y-axis.

To get this equation for this question, we need to find both m and c.

In order to do this, the formulas are given below:

While for c or the y-intercept, we have:

Before we can calculate m and c, we need to calculate the means of both x and y values give to us.

This is done below:

Now we can proceed to get the slope m of our line.

In order to be tidy, we shall use a table to solve. This table is shown in the image below:

Thus, we can now calculate our slope m:

Therefore the slope (m) = 0.34

Now to calculate intercept (c)

Therefore, the intercept (c) = - 0.9

Bringing it all together, we can write the equation of the line as:

y = 0.34x - 0.9

Therefore the answer is: y = 0.34x - 0.9 (Option A)

Given the expression (-x + 2y - 3z)², we are to expand it using a suitable identity.

Using the square of the sum of trinomial identity expressed as:

From the given expression;

Substitute the parameters into the identity to expand as shown:

Simplify the result to have:

This gives the correct expansion using a suitable identity

Natural numbers are just counting numbers. It doesn't include a negative number. Integers include both positive and negative whole numbers. rational numbers are fractions that can be expressed as two integers. We can have - 8/1 = - 8

Finally, real numbers is any positive or negative number. It includes integers and rational numbers. Therefore, the subset that contains - 8 would be

real, rational and integer numbers

Given:

Distance of top of ladder to the ground = 10 ft

Distance of bottom of ladder from the side of the house = 9 ft

Let's find the length of the ladder.

Since the ladder forms a right triangle with the house, to find the length of the ladder apply Pythagorean Theorem.

Where:

a = 10 ft

b = 9 ft

c = length of ladder

Thus, we have:

Take the square root of both sides:

Therefore, the length of the ladder rounded to the nearest tenth is 13.5 ft

ANSWER:

13.5 ft

From the given figures in the 2 triangles XYZ and ABC

mXZ = AC

m

Since we have two equal angles and the sides between them are equal, then

The 2 triangles are congruent using ASA postulate

The answer is C

To convert decimal numbers to percentage, what we need to do is to multiply the decimal number by 100, and we will get the representation as a percentage.

In this case we have the decimal number:

We multiply that number by 100 to write is as a percentage:

Answer: 75.1%

To solve this problem, we will first find the standard form of the circle equation. Given a circle of radius r and center (h,k), the standard form of the circle equation would be

In our case, we have h=8 , k=6 and r=10. So the equation for the given circle would be

The general form of the circle equation can be obtained from expanding the squares on the left side of the equality sign. Recall that

So, applying this to the standard equation we get

So our equation becomes

Operating on the left side, we have

By subtracting 100 on both sides, we get

which the general form of the equation of the given circle.

Using a graphing tool, we have that the circle's graph would be

You have the following expression:

"the sum of five squared and five"

the previous statement, in a mathematical form is:

5² + 5

It is important to point out that you have "the sum" of two numbers, which numbers? five squared and five.

The simplified form is:

5² + 5 = 25 + 5 = 30

Slope formula:

Replacing:

since x is constant , it is a vertical line, with an undefined slope.

She has already 500

x hours woked

pund we got:

7.50 x >= 900

And inequality could be

fx:o

because we need to gain 1400 or more

hours in order to have enough money to buy the computer

Sara needs to work at least 52 00/17.5

x >= 5r t o

The equatu

1

And then we can solve for x a

500+17.5x>>= 1400

utioen x

For this50 case we can do this:

500+ 17.

Area overall is 392 square metres. The two lawns' combined area is therefore 392 square metres.

A square is a quadrilateral in geometry that has four equal sides and four right angles (90-degree angles). It is a unique kind of both a rhombus and a rectangle. A square is made up of four equal-length sides, two equal-length diagonals, and right-angle diagonal cuts. A square's area and perimeter can be calculated by multiplying one of its sides by itself (squared), and one of its sides by four, respectively. Because of their symmetry and regularity, squares are frequently employed in mathematics and building.

given

By multiplying the first lawn's length by its breadth, one may determine its area: 56 square metres is the size of the first lawn, which is 8 metres by 7 metres.

The second lawn's breadth is six times that of the first lawn's, so:

The second lawn's width is equal to 6 × 7 metres, or 42 metres.

The second lawn is the same length as the first one, so:

The second lawn is 8 metres long.

The second lawn's area is calculated by multiplying its length by its width:

The second lawn is 336 square metres in size (8 metres by 42 metres).

The first and second lawns' combined areas make up the overall area of the two lawns:

Total area equals the sum of the first and second lawns.

56 square metres + 336 square metres make up the total area.

Area overall is 392 square metres. The two lawns' combined area is therefore 392 square metres.

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1) Considering the Revenue function in the standard form:

2) Since this is a quadratic function, we can write out the Vertex of this function:

3) So, we can answer this way:

The complementary angles are angles in which the sum of them is equal to 90º

So: 90º-10º=80º

So, the complementary angle is 80º

Statement Problem: Mr. Bensoua buys 3 bags of Flaming Hot Cheetos for every 4 bags of Takis. He buys a total of 14 bags of chips. If the Flamin Hot Cheetos cost $2 per bag and the Takis cost $2.50 per bag, how much did Mr. Bensoua spend on all of the chips?

Solution:

When Mr. Bensoua buys 4 bags of Takis, he buys 3 bags of Flaming Hot Cheetos.

When he buys another 4 bags of Takis, he buys 3 bags of Flaming Hot Cheetos.

At the end, he buys 8 bags of Takis and 6 bags of Flaming Hot Cheetos and that makes it a total of 14 bags of chips.

The cost of Takis per bag is $2.50, the cost of 8 bags of Takis is;

The cost of Flaming Hot Cheetos per bag is $2., the cost of 6 bags of Takis is;

Hence, the total amount Mr. Bensoua spends is;

CORRECT ANSWER: $32

0.3821,  0.8745

========================================================

Work Shown:

pi/2 = 3.14/2 = 1.57 approximately

The solutions for t must be in the interval 0 ≤ t ≤ 1.57

[tex]3\cos(5t)+3 = 2\\\\3\cos(5t) = 2-3\\\\3\cos(5t) = -1\\\\\cos(5t) = -1/3\\\\5t = \cos^{-1}(-1/3)\\\\5t \approx 1.9106+2\pi n \ \text{ or } \ 5t \approx -1.9106+2\pi n\\\\t \approx \frac{1.9106+2\pi n}{5} \ \text{ or } \ t \approx \frac{-1.9106+2\pi n}{5}\\\\[/tex]

where n is an integer.

Let

[tex]P = \frac{1.9106+2\pi n}{5}\\\\Q = \frac{-1.9106+2\pi n}{5}\\\\[/tex]

Then let's generate a small table of values like so

[tex]\begin{array}{|c|c|c|} \cline{1-3}n & P & Q\\\cline{1-3}-1 & -0.8745 & -1.6388\\\cline{1-3}0 & **0.3821** & -0.3821\\\cline{1-3}1 & 1.6388 & **0.8745**\\\cline{1-3}2 & 2.8954 & 2.1312\\\cline{1-3}\end{array}[/tex]

The terms with surrounding double stars represent items in the interval 0 ≤ t ≤ 1.57

Therefore, we end up with the solutions 0.3821 and 0.8745 both of which are approximate.

You can use a graphing tool like Desmos or GeoGebra to verify the solutions. Be sure to restrict the domain to 0 ≤ t ≤ 1.57

Answer:

[tex]\textsf{c)} \quad 0.3821, \; 0.8745[/tex]

Step-by-step explanation:

Given equation:

[tex]3 \cos (5t)+3=2, \quad \quad 0\leq t\leq \dfrac{\pi}{2}[/tex]

Rearrange the equation to isolate cos(5t):

[tex]\begin{aligned}\implies 3 \cos(5t)+3&=2\\3 \cos(5t)&=-1\\\cos(5t)&=-\dfrac{1}{3}\end{aligned}[/tex]

Take the inverse cosine of both sides:

[tex]\implies 5t=\cos^{-1}\left(-\dfrac{1}{3}\right)[/tex]

[tex]\implies 5t=1.91063..., -1.91063...[/tex]

As the cosine graph repeats every 2π radians, add 2πn to the answers:

[tex]\implies 5t=1.91063...+2\pi n, -1.91063...+2 \pi n[/tex]

Divide both sides by 5:

[tex]\implies t=0.38212...+\dfrac{2}{5}\pi n,\;\; -0.38212...+\dfrac{2}{5} \pi n[/tex]

The given interval is:

[tex]0\leq t\leq \dfrac{\pi}{2}\implies0\leq t\leq 1.57079...[/tex]

Therefore, the solutions to the equation in the given interval are:

[tex]\implies t=0.3821, \; 0.8745[/tex]

EXPLANATION

The value of the number in the hundreths place is 0.07

SOLUTION:

Step 1:

In question 12, we are meant to find the line of reflection for Triangle ABC and its image based on the diagram:

Step 2:

The line of reflection for Triangle ABC and its image is:

To solve the equation system by substitution, since the equations are expressed in terms of y, you have to equal both expressions and calculate the value of x:

To calculate the value of x, the first step is to pass the x-term to the left side of the equation by applying the opposite operation:

Next, pass 5 to the right side of the equation:

Finally, divide both sides by 6 to reach the value of x

Now that we have determined the value of x, replace it in either one of the original equations to determine the value of y:

The solution for this equation system is (2,1)

A line segment has the endpoints at (-6, -10) and (23, 6) then the midpoints of the line segment will be (17, -2).

An area or portion of a line with two endpoints is called a line segment. A line segment, in contrast to a line, has a known length. A line segment's length can be estimated by utilizing either metric measurements like millimeters or centimeters, or conventional measurements like feet or inches.

A line segment has the endpoints at (-6, -10) and (23, 6).

Mid point of the line segment is given by [tex]$\left(\frac{x_1+x_2}{2}\right),\left(\frac{y_1+y_2}{2}\right)$[/tex]

The midpoints of the line segment will be

=  [tex]$\frac{23+-6}{2}[/tex], [tex]$\frac{-10+6}{2}}[/tex]

= 17, -2

Therefore midpoints of the line segment will be (17, -2).

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The general formula for a quadratic equation is ax² + bx + c = 0.

To solve

You can follow the steps.

Step 01: Write the equation in the general formula.

To do it, add 3 to each side of the equation.

Step 02: Use the Bhaskara formula to find the roots.

The Bhaskara formula is:

In this question,

a = 2

b = 6

c = 2

So, substituting the values:

Answer:

Exact form:

Decimal form:

you would have to do this backwards

20 times 2 would remove the /2

5c=40

40 divided by 5

is

8

C=8