Cole hauls heavy equipment from North Dakota to Winnipeg. After crossing into Canada, he sees a sign that says the weight limit for the road is 7 metric tons. He must decide whether to drive on this road or to take a detour. How many U.S. standard tons are allowed on the road?

Answer:

-2,7

Step-by-step explanation:

[tex]\huge\bold\red{Answer:-}[/tex]

Step by step solution :

STEP 1 : Trying to factor by splitting the middle term

1.1 Factoring x2+5x-14

The first term is, x2 its coefficient is 1 .

The middle term is, +5x its coefficient is 5 .

The last term, "the constant", is -14

Step-1 : Multiply the coefficient of the first term by the constant 1 • -14 = -14

Step-2 : Find two factors of -14 whose sum equals the coefficient of the middle term, which is 5 .

-14 + 1 = -13

-7 + 2 = -5

-2 + 7 = 5 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and 7

x2 - 2x + 7x - 14

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-2)

Add up the last 2 terms, pulling out common factors :

7 • (x-2)

Step-5 : Add up the four terms of step 4 :

(x+7) • (x-2)

Which is the desired factorization.

Equation at the end of step 1 :

(x + 7) • (x - 2) = 0

STEP 2 : Theory - Roots of a product

2.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

2.2 Solve : x+7 = 0

Subtract 7 from both sides of the equation :

x = -7

Solving a Single Variable Equation:

2.3 Solve : x-2 = 0

Add 2 to both sides of the equation :

x = 2

Supplement : Solving Quadratic Equation Directly

Solving x2+5x-14 = 0 directly

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

3.1 Find the Vertex of y = x2+5x-14

For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is -2.5000

Plugging into the parabola formula -2.5000 for x we can calculate the y -coordinate :

y = 1.0 * -2.50 * -2.50 + 5.0 * -2.50 - 14.0

or y = -20.250

Parabola, Graphing Vertex and X-Intercepts :

Root plot for : y = x2+5x-14

Axis of Symmetry (dashed) {x}={-2.50}

Vertex at {x,y} = {-2.50,-20.25}

x -Intercepts (Roots) :

Root 1 at {x,y} = {-7.00, 0.00}

Root 2 at {x,y} = { 2.00, 0.00}

Solve Quadratic Equation by Completing The Square

3.2 Solving x2+5x-14 = 0 by Completing The Square .

Add 14 to both side of the equation :

x2+5x = 14

Now the clever bit: Take the coefficient of x , which is 5 , divide by two, giving 5/2 , and finally square it giving 25/4

Add 25/4 to both sides of the equation :

On the right hand side we have :

14 + 25/4 or, (14/1)+(25/4)

The common denominator of the two fractions is 4 Adding (56/4)+(25/4) gives 81/4

So adding to both sides we finally get :

x2+5x+(25/4) = 81/4

Adding 25/4 has completed the left hand side into a perfect square :

= x2+5x+(25/4)

= (x+(5/2)) • (x+(5/2))

= (x+(5/2))2

Things which are equal to the same thing are also equal to one another. Since

x2+5x+(25/4) = 81/4 and

x2+5x+(25/4) = (x+(5/2))2

then, according to the law of transitivity,

(x+(5/2))2 = 81/4

We'll refer to this Equation as Eq. #3.2.1

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

= (x+(5/2))2 is

= (x+(5/2))2/2

= (x+(5/2))1

=x+(5/2)

Now, applying the Square Root Principle to Eq. #3.2.1 we get:

x+(5/2) = √ 81/4

Subtract 5/2 from both sides to obtain:

x = -5/2 + √ 81/4

Since a square root has two values, one positive and the other negative

x2 + 5x - 14 = 0

has two solutions:

x = -5/2 + √ 81/4

or

x = -5/2 - √ 81/4

Note that √ 81/4 can be written as

√ 81 / √ 4 which is 9 / 2

Solve Quadratic Equation using the Quadratic Formula

3.3 Solving x2+5x-14 = 0 by the Quadratic Formula .

According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :

- B ± √ B2-4AC

x = ————————

2A

In our case, A = 1

B = 5

C = -14

Accordingly, = B2 - 4AC

=25 - (-56)

= 81

Applying the quadratic formula :

-5 ± √ 81

x = —————

2

Can √ 81 be simplified ?

Yes! The prime factorization of 81 is

3•3•3•3

To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).

√ 81 = √ 3•3•3•3 =3•3•√ 1

= ± 9 • √ 1

= ± 9

So now we are looking at:

x = ( -5 ± 9) / 2

Two real solutions:

x =(-5+√81)/2=(-5+9)/2= 2.000

or:

x =(-5-√81)/2=(-5-9)/2= -7.000

Two solutions were found :

Answer:

2x/3+6

Step-by-step explanation:

The quotient of twice a number and 3, is 2x divided by 3. Six more is 2x/3+6

Answer:

58

Step-by-step explanation:

Given :-

To solve :-

Solving :-

Answer:

58

is the final answer

Step-by-step explanation:

8(7)- (-2)=

56 +2= 58

Answer:

well u should go to sleep and get u some rest

Answer:

Perpendicular

Step-by-step explanation:

Remember that:

So, let's find the slope of QR and ST.

QR)

We can use the slope formula:

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

Let Q(-6, 11) be (x₁, y₁) and R(2, -1) be (x₂, y₂). Substitute:

[tex]m=\frac{-1-11}{2-(-6)}[/tex]

Subtract:

[tex]m=-12/8=-3/2[/tex]

So, the slope of QR is -3/2.

ST)

Let S(-4, 8) be (x₁, y₁) and T(-1, 10) be (x₂, y₂). Substitute:

[tex]m=\frac{10-8}{-1-(-4)}[/tex]

Subtract:

[tex]m=2/3[/tex]

So, the slope of ST is 2/3.

The negative reciprocal of -3/2 is 2/3.

And the negative reciprocal of 2/3 is -3/2.

So, the slopes are indeed negative reciprocals of each other.

So, QR and ST are perpendicular.

Perpendicular     hope this helped

37

Step-by-step explanation:

21 + 16

HOPE THIS HELPS!

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

Explanation:

The x coordinates of the two points are -6 and 4. They add to -6+4 = -2. Cut this in half to get -2/2 = -1.

The y coordinates of the two points are 3 and 9. They add to 3+9 = 12. Cut this in half to get 12/2 = 6.

The midpoint formula is

[tex]\left(x_m, y_m) = \left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)[/tex]

In short, you add the corresponding coordinates and then divide by 2.

Answer:

3

explanation:

[tex]\rightarrow \sf \sf \dfrac{36}{3a}[/tex]

[tex]\rightarrow \sf \sf \dfrac{36}{3(4)}[/tex]

[tex]\rightarrow \sf \sf \dfrac{36}{12}[/tex]

[tex]\rightarrow \sf \sf 3[/tex]

Answer:

The answer is A.

Step-by-step explanation:

3+6=9

-5-9=-14

-14/2

Hope this helps! :)

Answer:

Answer is A. -7

Step-by-step explanation:

-5-(3+6)/2. PEMDAS (Parenthesis)

-5-9/2 Add/Subtract & Slash and dash = -5 + -9 = -14

-14/7= -7/1 which is just -7

Answer:

x=33/5

Step-by-step explanation:

Let's solve your equation step-by-step.

2x+4/5 −6=8

Step 1: Simplify both sides of the equation.

2x+4/5−6=8

2x+4/5+−6=8

(2x)+(4/5+−6)=8(Combine Like Terms)

2x+−26/5=8

2x+−26/5=8

Step 2: Add 26/5 to both sides.

2x+−26/5+26/5=8+26/5

2x=66/5

Step 3: Divide both sides by 2.

2x/2=66/5/2

x=33/5

Answer:

a = 8/3b or b = 3/8a

Step-by-step explanation:

The fractions present in the table, 24/9 and 40/15, are equivalent to 8/3, showing a linear relationship between the variables a and b. Knowing this, reducing any of the 3 fractions to its lowest form will allow you to find the information necessary to develop an equation. As 8/3 turns out to be the simplest form of any of the fractions, the equation is a = 8/3b, or, if you decide to reverse the variables, b = 3/8a.

Answer:

c, d, and h are parallel

Step-by-step explanation:

parallel lines are when the slope is the same and the y-intercept is different

a. y = 2x - 3

b. y = -3x + 7

c. y = -2x + 4

d. y = -2x + 2

e. y = 1/3x - 3

f. y = x/2 + 7/2

g. y = -x/3 + 8/3

h. y = -2x + 5

c, d, and h all have the same slope of -2 and contain different y-intercepts

Answer:

C: (4,5)

Step-by-step explanation:

The solution is where the two lines intersect.

Answer:

exact form:

x=±√5+1

decimal form:

x = 3.23606797..., -1.23606797...

Step-by-step explanation:

Use the formula (b/2)^2 in order to create a new term. Solve for x by using this term to complete the square. ---- :))

Answer:

x = √5 + 1, x = -√5 + 1

Step-by-step explanation:

We want the coefficient of x^2 to be 1, so let's divide either side by 3;

3x^2 - 6x - 12 = 0 => Divide either side by 3

3x^2/3 - 6x/3 - 12/3 = 0/3 => Simplify

x^2 - 2x - 4 = 0

Let's try to form a perfect square;

(x^2 - 2x + ? ) - 4 = 0

          |

         1/2(- 2) = (- 1)^2 = 1

(x^2 - 2x + 1) + 4 - 1 = 0

(x - 1)^2 - 5 = 0

(x - 1)^2 = 5

For x - 1 = √5 : x = √5 + 1

For x - 1 = - √5 : x = -√5 + 1

9514 1404 393

Answer:

Step-by-step explanation:

1. The common difference is -4, which matches recursive relation A.

2. Signs alternate, so the common ratio must be negative, matching recursive relation C.

3. The common difference is 0, and the common ratio is 1, so both relations B and D are a match.

_____

An arithmetic sequence with common difference d can be described by the recursive relation ...

  f(n) = f(n-1) +d

A geometric sequence with common ratio r can be described by the recursive relation ...

  f(n) = r·f(n-1)

One typically has to look at only the first three terms to determine if they have a constant difference or a constant ratio.

Answer:

the answer is 4

Step-by-step explanation:

Answer:

13+5-14 is equaled to 4 so if i do 18-14 is will still give me 4 because 13+5 is 18 so 18- 14 is 4

Perimeter:

[tex]6y + 12[/tex]

Area:

[tex] {2y}^{2} + 12y[/tex]

Step-by-step explanation:

Perimeter of a rectangle : P= 2( L + w)

in this case it would be 2(y+6) + 2(2y)

= 2y+12 + 4y

simplified to 6y +12

Area of a rectangle : A= LW

=(y+6)(2y)

We foil and get

[tex] {2y}^{2} + 12y[/tex]

30% of the final exam

70% of final exam:-

Answer:

A: 2/3, B: 5, C: Yes because the slope is consistent.

Step-by-step explanation:

Answer:

table, graph or equation

Answer:

$855.00

Step-by-step explanation:

85.50 x 15 = 1,282.50

2,137.50 - 1,282.50 = 855.00

The percent Jan’s total grocery bill discounted when she bought no items on sale is 16.65%.

Percentage of a number is the part of the number expressed in the in every hundred. Percentage of a number is expressed with the symbol '%'.

Jan went grocery shopping and only bought items which had been marked down.

The items she bought, along with their prices, can be seen below.

Total price of the items is $18.72. Now find out the original price using the above formula for each of the item. The sum of original price of all the items will be $22.46.

Thus, the discounted price will be,

[tex]P_d=\dfrac{18.72}{22.46}\times100\\P_d=83.35\%[/tex]

The overall markdown is,

[tex]\rm Markdown=100-18.35\\\rm Markdown=16.65\%[/tex]

Thus, the percent Jan’s total grocery bill discounted when she bought no items on sale is 16.65%.

Learn more about the percentage here;

https://brainly.com/question/24304697

Answer:

£ 45.6

Step-by-step explanation:

Number of adults ⇒ 12

Number of children ⇒ 26

Total cost of tickets ⇒ £ 1804.80

Cost of an adult's ticket ⇒ £ 51.60

Cost of a ticket for child ⇒ ?

Let the cost of a ticket for child be x.

Therefore,

Total cost = cost of tickets for adults + cost of tickets for children

Total cost = (No. children × Cost of a ticket) + (No.adults × Cost of a ticket)

£ 1804.80 = 26x + 12 × £51.60

1804.80  = 26x + 619.2

1804.80 - 619.2 = 26x

1185.6 = 26x

Divide both sides by 26.

45.6 = x

So,

Cost of a ticket for child is £45.6

Step-by-step explanation:

12 x 51.60 you get the total cost for the adult tickets and all thats left is the total cost - adult ticket cost and then you get the child ticket wirth now all thats left is childs ticket cost % 26

Answer:

$17.54

Step-by-step explanation:

Given the following question:

25% of 70.16

To find the answer we simply use the formula to calculate percentages to find 25% of 70.16. Of course, round if needed.

[tex]\frac{p\times n}{100}[/tex]
[tex]\frac{25\times70.16}{100} =1754\div100=17.54[/tex]
[tex]=17.54[/tex]

The sleeping bags shipping, and handling will cost "$17.54."

Hope this helps.

Answer:

=12x+28

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

it wouldn't be asking for a second copy of your records, but both , making sure that the items charged are the same as the items received and Checking to see if all of the discounts were applied properly is correct

Answer:

im not sure but i could try and work it out

Using the slope concept, it is found that the medic was 370.5 ft from the shelter.

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

In this problem:

Hence:

[tex]\tan{65^\circ} = \frac{794.5]{d}[/tex]

[tex]d = \frac{794.5}{\tan{65^\circ}}[/tex]

[tex]d = 370.5[/tex]

The medic was 370.5 ft from the shelter.

More can be learned about the slope concept at https://brainly.com/question/18090623

Answer:

The answer is True.

Step-by-step explanation:

-3x - 10 > -31

-3(5) - 10 > -31

-15 - 10 > -31

-25 > -31

True.

Answer: 28 feet and 4.5 inches

8 meters = 26.24...

.650 meters = 25 inches.

25 inches = 2 feet 1 inch

28 and 4.5 inches is your answer.