shania traveled 310 miles in 5 hours. if she remain at a constant rate , how many miles can she travel in 1 hour

To answer this question, we need to know that we can represent, algebraically, two consecutive positive odd numbers as follows:

Then, if we have that the product of both consecutive positive odd numbers is 323, then:

Now, we will need to expand the formula as follows:

We applied the FOIL method to expand the expression. Then, we have:

Now, we have:

We have here a polynomial (a quadratic equation) that we can solve using the quadratic formula:

Then, we have that:

• a = 4

• b = 8

• c = -320

Then

Then, the solutions are:

Therefore, we have two solutions for n, n = 8 or n = -10.

If we substitute the value of n = 8 in the original equations, we have:

If we use the negative value for the solution, we obtain:

Since these two numbers are negative, we have that the appropriate solution is n = 8.

Therefore, we have that the smaller of the two numbers is 17:

The numbers 17 and 19 are consecutive positive odd numbers.

In summary, we have that the smaller number is 17.

m∠A of the given rectangular triangle is 74.05°.

Given :

a = 7

b = 2

∠c =90°

according to Pythagoras theorem  

c =[tex]\sqrt[n]{a^2 + b^2}[/tex]

c = [tex]\sqrt{7^2 + 2^2}[/tex]

c≈7.28011.

to  find m∠A

Sin A = [tex]\frac{opp. side}{Hypotenuse}[/tex] = 7/7.28011 = 0.9615

∠A = sin⁻¹ 0.9615

m∠A = 74.05°.

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Step 1

Given;

Required; To multiply the polynomials

Step 2

Write the answers in standard form.

Rearrange the question and write like terms close to each other

Simplify using the following law of indices

Hence the combined answer will be;

Answer;

The general form of a quadratic is:

We need to plug in the 3 pair of points into "x" and "y" and simultaneously solve the 3 equations for a, b, and c.

Putting (0,9):

Putting (-6,9):

Putting (-5,4):

We substitute a=b/6 into this equation and solve for b:

Thus, "a" will be:

Thus, we have a = 1, b = 6, c = 9

The equation is:

ANSWER :

a. 628 cubic foot

b. 52 cubic foot

c. 1.17 ton

EXPLANATION :

The volume formula of a cylinder is :

The volume formula of a cone is :

From the problem, we have a diameter of 10 ft, so the radius is r = 5 ft

Cylinder's height is 8 ft and cone's height is 2 ft

a. volume of cylinder part :

b. volume of cone part :

c. The combine volume is 628 + 52 = 680 cubic foot

A dry corn weighs 45 lbs per cubic foot.

That will be :

There are 2000 pounds per ton, so that will be :

The area of the inner section is 320 cm^2

The area of the bigger section is 96 cm^2 (bigger trapezoid)

The area of the smaller trapezoid is 80 cm^2

Here, we want to calculate the area of each section of the frame

As we can see, there are 5 sections of the frame

The inner section represented by a rectangle and 4 adjoining shapes looking like a trapezoid

The inner part of the frame is a rectangle that measures 16 cm by 20 cm

Now, for the trapezoid part, we have 2 different sets

The first two set, has a longer length 28 cm, and shorter length of 20 cm

The second set has a longer length of 24 cm and a shorter length of 16 cm

Now, to get the area of the trapezoid, we need the height of the trapezoid which is called the width in this case. This measure corresponds to a measure of 4 cm on the two sets

Mathematically, the area of a trapezoid is;

Where a is the longer length and b is the shorter length with h representing the width of 4 cm

For the bigger trapezoid, we have;

For the smaller trapezoid, we have;

Then, we have the inner section as;

Mark has ten pens.

Kate has 5 times as many pens as mark has

Number of pen kate has = 5 (number of pens of Mark)

y is the number of Kates pen

y = 5( Number of pens of Mark)

y=5(10)

y= 5 x 10

Answer : C) y = 5 x 10

Answer:

Where is the math question?

The probability of getting a black sock out of the drawer is given by the ratio between the amount of black socks in the drawer by the total amount of socks in the drawer.

We know that we have 3 black socks, now we just need to calculate the total amount of socks. We have three black, four white, two blue, and four gray socks in a drawer, then, the total is given by

We have a total of 13 socks in the drawer, therefore, the probability of getting a black sock out of the drawer is given by

And this is the fraction in the most simplified version.

Answer:

Through any two points there is exactly one plane.

Step-by-Step explanation:

Postulate: Statement that is believed to be true, just without proof.

The first one is correct, that is, it is a true postulate.

The third statement is correct.

The fourth statement is also correct.

The answer is the second postulate.

It is stated that:

Through any two points there is exactly one plane.

But the correct postulate is:

Through any two points there is exactly one line.

So the answer is:

Through any two points there is exactly one plane.

The solution of the simultaneous equation using substitution is

(x ,y) = (-9,-4) .

The given system of equation are:

x=-9............................................1

-4x+4y=20 ...............................2

Now we will simplify the equation 2

or, -x + y = 5

now we will substitute the value of x in the equation 2

or, -(-9) + y = 5

or, 9+ y= 5

or, y = -4

Two or more algebra equations that share variables, such as x and y, are said to be simultaneous equations. Since the equations are resolved simultaneously, they are known as simultaneous equations. Each equation represents a straight line.

These equations alone could have an endless number of solutions. There are several ways to solve the simultaneous linear equations.

The simultaneous equations can be solved using one of four methods:

Hence the values of x and y are -9 and -4 respectively.

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Find the derivative of S(t)=70-20ln(t+1)

The derivative is -20/t+1

Let's write the equation for every function:

Since f(x) passes through (0,-1) and (5,14), the equation will be given by:

Using the point-slope equation:

Using the same procedure for g(x):

Now we have our functions:

Part A:

We can translated f(x) k units up in order to get g(x) ( A vertical translation)

Or, we can translated f(x) k units to the left in order to get g(x) ( A horizontal translation)

We can see a graph of the functions:

Where the red function is f(x) and the blue function is g(x).

Part B:

Since both functions must be equal:

Solve for k:

-----------------------

For the other case, let's use the same procedure:

Part C:

For the vertical translation:

For the horizontal translation:

From the trapezoid,

x + ( 31 + 38 ) + y = 180 ------------ equ 1

x + y + 69 = 180

x + y = 180 - 69

x + y = 111 .................... equ 2

Also, x + 31 + 90 = 180

x + 121 = 180

x = 180 -121

x = 59.....................equ 3

put x = 59 in equ 2 ,

59 + y = 11

y = 111 - 59

y = 52 ------------------equ 4

A unit circle is a circle with a radius of 1 unit.

The angle θ = 30⁰'

The terminal points are:

1) Comparing those Mixed numbers we can stat which is greater, lesser than, or equal by dividing the numerator by the denominator and adding to the whole number:

So there are cases when the fraction is the same we just need to compare the whole number.

But in most cases, dividing the numerator by the denominator and writing it as a decimal number is really helpful

3) So the answers are:

Answer:

D. y=875(1.02)^x

Explanation:

Initial population = 875 people

Growth rate = 2%

The population after x years can be modeled below:

The correct choice is D.

1) In this problem, let's solve this given system of equations by the method of Elimination.

We can start by adding both equations simultaneously:

Now, that we know the quantity of x, let's plug it into any of those equations. Most of the time, we opt to plug it into the simpler equation.

2) Thus, the answer is (4,0)

Given two triangles ABC and DEF

They have the following:

1. AC = DF

2. 3. AB = DE

4.

so, if we take 1, 2 and 3

the triangles are congruent using SAS

And if we take 1 , 2 and 4

the triangle are congruent using ASA

So, the answer is the options: D and E

From the question, there are some scenarios we need to cater for:

- The team is down 14 points.

- It is a given that the team scores 2 touchdowns whatever the case. This means the team has 12 points in the bag.

- That leaves 2 points to overturn the loss, or draw or lose

If the team wins:

The team can only win if they score their 2 points runs twice. i.e. An increase in 4 points from the two plays would overturn the score and the team would lead the game by 2 points.

The question asks us to find the probability of the team winning if the team goes for 2 points after each 6-point touchdown.

We can solve this as:

If the team loses:

If the team loses, there are some scenarios to take into consideration:

1. If the team tries 1 point plays and succeeds one time and failing the other time

2. If the team tries 1 point plays and fails twice.

3. If the team tries 2 point plays and they fail twice. (i.e. if they succeed even once, they can draw the match

Let's solve the equation for y:

Therefore we have:

For this equation we have that the slope is 2 and the y-intercept is 8.

The value of x can be determined as,

In triangle ABC,

We chave 9 purple cups and 10 green cups, so we can write the ratio between purple and green cups as 9:10 or "9 to 10".

Answer: 9:10

As the given lines are:

To find the system of linear equation:

multiply equation (1)by 3 and then add in equation 2:

Now put the value of x in equation 1:

We know that the area of a square is 49 square meters.

The area of a square is defined by

Where l is the length of each side.

Replacing the given are, we have

anIf we have an equation of the form

then the equation of the perpendicular will be

where c is any arbitrary constant determined by the point the line must pass through,

Now in our case, we have

Therefore, the equation of the perpendicular line will be

We must choose c such that the above line passes through (-2,2).

Putting in y = 2 and x = 2 from (-2, 2) gives

Hence, the equation of a line perpendicular y = -10x + 20 and passing through (-2, 2) is

Now we find the equation of a line parallel to y = -10x+20 and passing through (-2,2).

Now, the slope of the parallel line is the same as that of the original equation; therefore the equation for the parallel line we have is

We find k by using the point (-2,2) and substituting x = -2 and y = 2 into the above equation to get

Hence, the equation of the parallel line is

Since the graphs are parallel to each other, there is no solution to the system. If a system has no solution, it is said to be an inconsistent system. So, the given system is inconsistent.

Solution

An algebraic fraction is a fraction whose numerator and denominator are algebraic expressions.

Algebraic fractions are fractions that contain variables, exponents, and operations with polynomials.

O True Answer

O False

to determine the lcm of 6 and 8, express these numbers as the product of prime numbers:

6 = 2x3

8 = 2x2x2

the same factors determine the lcm. In this case, the factors

It is given that four friends collected 9 1/3 bags of treats.

Now 28/3 bags divided equally among 4 friends will be:

Hence the total number of bags that each person will receive is 7/3 bags or 2 1/3 bags.

The allowable values are;

Here, we want to get the allowable values for the given information

To do this, we need to find the percentage value

That would be;

Now, the allowable values can be in both direction

Greater than 50 or less than 50

When greater, we add; when lesser, we subtract

Thus, we have it as;