MATHEMATICS HIGH SCHOOL

Write the perimeter of the floor plan shown as an algebraic expression in x.

Answers

Answer 1

Answer:

Answer:

Perimeter = 2x + 64

Step-by-step explanation:

Perimeter = Sum of the lengths of the borders

From the given figure, we need to find the missing length.

Missing length = 18 - 10 = 8

Another missing length = (x + 14) - (x + 8) = x + 14 - x - 8

= 14 -8

= 6

Now let's add all the sides.

Perimeter = x + 14 + 8 + 6 + 10 + x + 8 + 18

Now add all the x terms and constants

Perimeter = 2x + 64

Answer 2

Answer: I believe the answer is --> p(perimeter) = 2x + 64 in the simplest algebraic expression.

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There are chickens and pigs in a farm yard? There are 68 feet and 23 tails in the farm yard. How many chickens and how many pigs does grandma have?

Answers

You have animals with 4 legs, and animals with 2 legs. Both animals only have one tail. So, given that they only have one tail, there are only 23 animals in the farmyard.
Now, the equation would be,
$(68)/(x) =23$
$68=23x$
$(68)/(23) =x$

Answer:

12 chickens and 11 pigs

Step-by-step explanation:

We know that...

Chickens have 2 feet and 1 tail.

Pigs have 4 feet and 1 tail.

Let c represent chickens.

Let p represent pigs.

We need to create two equations. One for feet, and one for tails.

Tails:

Because each animal has 1 tail, we can say that the number of pigs, (p) plus the number of chickens, (c) must equal 23. So...

c + p = 23

Feet:

Because each chicken has two feet, and each pig has 4 feet, we can say that 2 times the number of chickens, (c) plus 4 times the number of pigs, (p) needs to equal 68. So...

2c + 4p = 68

Now we have two equations.

2c + 4p = 68

and

c + p = 23

We can use the substitution method to find c and p. The substitution method involves solving for one of the variables with one of the equations, then placing it into the other equation, so that you only have one variable to solve for, which you can do with simple algebra.

Solve for c

c + p = 23

c = 23 - p

Add that to the other equation.

2c + 4p = 68

2(23 - p) + 4p = 68

Solve for p

46 - 2p + 4p = 68

46 + 2p = 68

2p = 22

p = 11

Now that we know p, we can plug that into one of the equations to find c.

c + p = 23

c + (11) = 23

c = 12

Now we have c and p.

There are 12 chickens and 11 pigs on the farm.

Craig has £13.40 he sees this offer in a restaurant :main courses £8.90 each.Buy one main course and get the second half price. Can he afford to buy two main courses?Show your working

Answers

Answer:

Yes

Step-by-step explanation:

Full price for first course: £8.90

Half price: £4.45

One and one half times

full price is then: £13.35

Since this is less than Craig's £13.40, he can just barely afford to buy two main courses at these prices.

The length of a rectangle is represented by (6x − 2), and the width is represented by (x − 1). Which expression best represents the area of the rectangle?

Answers

The are of a rectangle can be obtained by using the formula

A=L*W

Since we are already given with the L, which is (6x-2), and the width, which is (x-1), the area of the rectangle is then

A = (6x-2)(x-1)

which, upon further simplification will give us

A = 6x^2-2x-6x+2

Combining like terms will yield

A = 6x^2-8x+2

Hence, the area of the specified rectangle is represented by the expression 6x^2 -8x +2.

The expression for the area of the rectangle is 6x²-8x+2.

What is area?

This is the region or space bounded by a plane shape.

To calculate the expression for the area of the triangle, we use the formula below

Formula:

A = lw............... Equation 1

Where:

A = Area of the rectangle
l = Length of the rectangle
w = Width of the rectangle.

From the question,

Given:

l = (6x-2)
w = (x-1)

Substitute these values into equation 1

A = (6x-2)(x-1)
A = 6x²-6x-2x+2
A = 6x²-8x+2

Hence, the expression for the area of the rectangle is 6x²-8x+2.

Learn more about area here: brainly.com/question/17713367

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Simplify the expression. log(1/7)

Answers

Answer:

d. $(1)/(7)$

Step-by-step explanation:

The given logarithm is

$10^{\log((1)/(7))}$

Recall that the common logarithm has a base of 10.

$10^{\log((1)/(7))}=10^{\log_(10)((1)/(7))}$

Recall also that; $p^((\log_pa))=a$

$10^{\log((1)/(7))}=10^{\log_(10)((1)/(7))}=(1)/(7)$

Rewrite the equation 11 x - 5 x 2 + 7 = 6 in standard form and identify a, b, and c

Answers

Answer:

5x^2 - 11x = 1

This is now in standard form, where a = 5, b = -11, and c = 1.

Step-by-step explanation:

To rewrite the equation 11x - 5x^2 + 7 = 6 in standard form, we need to rearrange the terms so that the polynomial is in descending order of degree, with no missing terms. The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.

So, let's start by moving the constant term to the right-hand side of the equation:

11x - 5x^2 = 6 - 7

11x - 5x^2 = -1

Next, we can multiply both sides of the equation by -1 to make the coefficient of the x^2 term positive:

5x^2 - 11x = 1

This is now in standard form, where a = 5, b = -11, and c = 1.

10 2.5 16 4 ? 7.5 48 12 Which statement explains how to find the number of minutes it takes to bike 7.5 miles? Find the ratio of minutes to miles, 4:1. Divide 7.5 by 4. Find the ratio of minutes to miles, 4:1. Multiply 7.5 by 4. Find the difference between 16 and 10. Add the difference to 16. Find the difference between 16 and 10. Add the difference to 7.5.