1
The diagram below shows the length and width of the wall
that Tara is going to cover with wallpaper.
24 feet
(15 feet
What is the least amount of wall paper Tara will need to
cover the entire area of the wall?
A 39 square feet
C 350 square feet
B 78 square feet
D 360 square feet

Answer:

answer 1: It forms a linear pair with one of the interior angles of the triangle

Step-by-step explanation:

The sum of an exterior angle and its adjacent interior angle is 180 degrees.

Also, linear pair of angles are supplementary.

Answer:

1. x > 13

2. x < -2

3. x < 5

Step-by-step explanation:

2x - 3 > 23

→Add 3 to both sides:

2x > 26

→Divide both sides by 2:

x > 13

2x - 3 > 3x - 1

→Subtract 2x from both sides:

-3 > x - 1

→Add 1 to both sides:

-2 > x

5x - 4 < 21

→Add 4 to both sides:

5x < 25

→Divide both sides by 5:

x < 5

Answer:

For real

Step-by-step explanation:

Answer:

x = -24/7  or x = -3 3/7

Step-by-step explanation:

In this equation, the first thing we will do is to get rid of the denominators -- they complicate everything. So, we can multiply the entire equation by 10, since 10 is the lowest common multiple of 5 and 2, which are the denominators.

Then, the equation will look like this:

2(4x-2) + 5(1) = 5(3x+7) - 10(1)

Notice that the denominators will no longer exist.

Now, distribute on both sides of the equation.

The equation will look like this now:

8x - 4 + 5 = 15x + 35 - 10

Then, we must combine like terms. We want to isolate the variable x on one side of the equation. Let's isolate it on the right side. So, subtract 8x from both sides. The equation will look like this now: - 4 + 5 = 7x + 35 - 10

Now that x is on one side, let's move all the other terms to the left side. Subtract 25 from both sides (35 - 10 = 25 on the right side, get rid of it by subtracting 25). The equation now looks like this: - 4 + 5 - 25 = 7x

Finally, combine all on the left side.

Final equation: -24 = 7x

Now, we know 7x = -24. We want to solve for the value of x. So, divide both sides by 7.

x = -24/7  or x = -3 3/7

Answer:

[tex] 5 - 2 \sqrt{6} [/tex]

Step-by-step explanation:

Perhaps you are interested in rationalising the denominator of the given problem. Let's do it.

[tex] \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \\ \\ multiplying \: numerator \: and \: denominator \: \\ by \: (\sqrt{3} - \sqrt{2}) \\ \\ \frac{( \sqrt{3} - \sqrt{2} ) }{ (\sqrt{3} + \sqrt{2} )} \times \frac{ (\sqrt{3} - \sqrt{2} )}{ (\sqrt{3} - \sqrt{2} )} \\ \\ = \frac{{( \sqrt{3} - \sqrt{2} )}^{2} }{ { (\sqrt{3} })^{2} - {( \sqrt{2} })^{2} } \\ \\ = \frac{ { (\sqrt{3} )}^{2} + { (\sqrt{2} )}^{2} - 2 \sqrt{3 \times 2} }{3 - 2} \\ \\ = \frac{3 + 2 - 2 \sqrt{6} }{1} \\ \\ = 5 - 2 \sqrt{6} [/tex]

Equilateral triangles have 3 sides of the same length, so if you split it down the middle, you will end up with one side length of 10cm and another with 5cm. Pythagorus can be used to find the missing side length, because the line of symmetry creates a right angle.

a^2 + b^2 = c^2

5^2 + b^2 = 10^2       (substitute given values in, remember the longest side, or the side opposite the right angle is c)

25 + b^2 = 100          (simplify)

b^2 = 75

b =  8.6603

Check answer

5^2 + 8.6603^2 = 10^2

25 + 75 = 100

Answer:

Step-by-step explanation:

Given

  Fantasy uses 4 lb of nuts, 3 lb of chocolate, for a profit of $50

  Ecstasy uses 4 lb of nuts, 1 lb of chocolate, for a profit of $40

  In stock are 16 lb of nuts, 10 lb of chocolate

Find

 amount of each to maximize profit

Solution

Let x and y represent barrels of Fantasy and Ecstasy, respectively. Then the limitations on production are ...

  4x +4y ≤ 16 . . . lb of nuts

  3x +y ≤ 10 . . . . lb of chocolate

We want to maximize

  50x +40y

The graph shows the feasible region. Its vertices are ...

  (0, 4), (3, 1), (3.33, 0)

Profit is maximized at $190 when production is 3 barrels of Fantasy and 1 barrel of Ecstasy.

Answer:

Domain: the set of “Pregant Sheep”

Range: the set of “Lambs Born”

Exaplain why your Relation is a Function.

“The reason it‘s a function is the fact that there is two parents (if you include the dad) and you can have one to three lambs born.  

Step-by-step explanation:

We want to write a real-world example of a relation that is a function.

First, let's describe what a function is.

A function is a relationship that maps elements from a set, the domain, into elements from another set, the range.

Such that each element in the domain can be mapped into only one element in the range.

So for example, if for a given item we have 2 different prices, like:

this is not a function, because the input "bar of soap" is being mapped into two different elements of the range.

Now that we know what a function is, we can create a real-world example.

Let's create a really simple one, let's say that in your local store they sell each bar of soap for $2.

Then, if you buy x of these, the cost will be x times $2, or:

$2*x

Then we can create a function, the cost function, that models the cost of buying x bars of soap at your local store, it is:

c(x) = $2*x

This is a function that models a "real-world" problem.

If you want to learn more, you can read:

https://brainly.com/question/183587

Answer:

384 cm³

Step-by-step explanation:

To find the volume of raspberries in Kendrick's box you have to use the formula to calculate the volume of a box:

V= l*w*h, where

l=Length: 8 cm

w=width: 8 cm

h= height: 6 cm

Then, you can replace the values in the formula:

V= 8cm*8cm*6cm

V=384 cm³

According to this, the answer is that the volume of raspberries in Kendrick's box is 384 cm³.

Answer: The answer is 7x.

Step-by-step explanation:

Answer:

The answer is x=9 and y=1

Step-by-step explanation:

First, you have to substitute x from -4x to 9y which is -4(9y).

That would equal -36y.

Then the second equation would look like this:

-36y + y = -35

Then simplify. If you add -36y and y, it would equal -35y.

-35y = -35

Divide -35 on each side.

y = 1

To find the x value, you have to plug 1 into the first equation. (It doesn't matter which equation you plug into).

So if you plug it into the first equation it would look like this:

9(1) = x

9 = x

Answer:

it might be trinomial if not maybe its monomial hope it helps ;/

Step-by-step explanation:

Answer:

1/2(6)(2 + x) = 27

3(2 + x) = 27

6 + 3x = 27

6 - 6 + 3x = 27 - 6

3x = 21

3x / 3 = 21 / 3

x = 7

Step-by-step explanation:

Answer:

Step-by-step explanation:

Use the formula A = a + b/2 · h

b = 2·A/h - a

b = 2 · 27/6 - 2

b = 7

Answer:

[tex]m\widehat {EB}[/tex] = 96°

Step-by-step explanation:

From the figure attached,

m∠ECB = 25°

[tex]m\widehat {EB}={(4x+16)}[/tex] degrees

[tex]m\widehat{DB}=(7x+6)[/tex] degrees

From the theorem of secants intersecting outside the circle,

m∠ECB = [tex]\frac{1}{2}[m\widehat {DB}-m\widehat{EB}][/tex]

25° = [tex]\frac{1}{2}[(7x + 6) - (4x + 16)][/tex]

25° = [tex]\frac{1}{2}(3x-10)[/tex]

50 = 3x - 10

3x = 60

x = [tex]\frac{60}{3}[/tex]

x = 20

[tex]m\widehat {EB}[/tex] = (4 × 20 + 16)°

        = (80 + 16)°

        = 96°

Therefore, measure of arc EB is 96°.

Answer:

96°

Step-by-step explanation:

Got it right on the test

Answer:

c

Step-by-step explanation:

Answer:

514,400 plants.

Step-by-step Explanation:

From the attached diagram given below which shows the coordinate grid, we can say the shape of the farm is that of a trapezium.

Number of plants to be planted by the farmer at 40,000 plants per acre = area of land in acres * 40,000.

Let's find the area of the land(trapezium):

Area of trapezium = ½(a+b)*h

From the coordinate grid, from point E to H on the y-axis, we have 900 units = 900 ft (Given that 1 unit = 1 foot).

Also, from F to G, we have 500 units = 500ft; and the height of the trapezium is represented by the number of units the trapezium covers on the x-axis = 800units = 800ft.

a = 900ft, b = 500ft, c= 800ft

==> Area of Land/trapezium = ½(a+b)*h

= ½(900+500)*800

= ½(1400)*800

= 700*800 = 560,000ft²

Given that 1acre = 43,560ft²

x acre = 560,000ft²

x = 560,000*1 /43,560

x = 12.86 acres

Therefore, number of plants to be planted = 12.86 acres * 40,000 plants = 514,400 plants.

Answer:

4.176  × 10¹⁵

Step-by-step explanation:

2.9×10⁵×7.2×10²÷5×10^-8=

2.9×7.2×10⁷×10⁸ / 5=

4.176  × 10¹⁵

Answer:

Find the exact value using trigonometric identities. a MP3, 45, 0.15

Step-by-step explanation:

so your answer is $45.15 that is how much it was before the discount :)

Answer:

$8.25

Step-by-step explanation:

discount = x

original price = $45.00

discount% = 15%

x/45 = 15/100

x · 100 = 15 · 45

100x = 675

100x/100 = 675/100

x = 6.75

Sale price = 15 - 6.75 = 8.25

Answer:

65/9

Step-by-step explanation:

3 1/3=(3*3+1)/3=10/3

2  1/6=(2*6+1)/6=13/6

10/3*13/6=130/18=65/9

Answer:

[tex]7\frac{2}{9}[/tex]

Step-by-step explanation:

[tex]3 \frac{1}{3} = \frac{10}{3}[/tex]

[tex]2\frac{1}{6} = \frac{13}{6}[/tex]

10 × 13 = 130

3 × 6 = 18

[tex]\frac{130}{18} = 7\frac{2}{9}[/tex]

Answer:

We are given that triangle PQR is an isosceles triangle in which PQ = PR .

Since the base angles of an isosceles triangle are equal,

angle PQR = angle PRQ  

Also, And we are given that

angle MRQ = angle NQR

In ΔQNR and  ΔRMQ

∠NQR=∠MRQ (given)

QR = QR   (common)

-triangles QNR is congruent to triangles RMQ - ASA - angle side angle

Answer:

F(x) = (x + 3)^2 -87

Step-by-step explanation:

Here, we want to rewrite the function by completing the square.

Firstly, we move the c term(-78) to the right hand side of the equation and that becomes

x^2 + 6x = 78

Then, we can complete the square on the right hand side here, to be

Let’s add 9 to both sides

That would be;

x^2 + 6x + 9 = 78 + 9

x^2 + 6x + 9 = 87

(x+3)^2 = 87

or simply

(x+3)^2 -87 = 0

So our F(x) becomes

F(x) = (x + 3)^2 -87

Answer:

The expression after completing the square is:

[tex]f(x) = (x+3)^{2} -87[/tex]

Step-by-step explanation:

The function is rewritten after making algebraic manipulation:

[tex]f(x) = x^{2} + 6\cdot x +9 - 9 - 78[/tex]

The expression after completing the square is:

[tex]f(x) = (x+3)^{2} -87[/tex]

Answer:

you should be able to use them

Step-by-step explanation:

Answer:

135, 137, 139

Step-by-step explanation: My bad, I did not see that it said consecutive odd integers

x+x+2+x+4=411

3x+6=411

3x=405

x=135

x+2+137

x+4=139

Represent 3 consecutive odd integers as follows.

X ⇒ first odd integer

X + 2 ⇒ second odd integer

X + 4 ⇒ third odd integer

Since their sum in this problem is 411, x + (x + 2) + (x + 4) = 411.

Now combine like terms to get 3x + 6 = 411.

No subtract 6 from both sides to get 3x = 405.

Now divide both sides by 3 and x = 135.

So x + 2 would be 137 and x + 4 would be 139.

So our consecutive odd integers are 135, 137, and 139.

Answer:

n = 5  or  n = -5

Step-by-step explanation:

Absolute value means take the non negative value

|n| = 5

n = 5   n = -5

Answer:

5

Step-by-step explanation:

Answer:

I think

all the rectangle in the shape u have to find the area of the rectangle

55×55 for each rectangel \ l ×W

now do the squares

25×25 for each rectangle

now when u got all the sides add them up

Answer:

11 + x m

Step-by-step explanation:

[tex]width = \frac{area \: of \: rectangle}{length} \\ \\ = \frac{121 - {x}^{2} }{11 - x} \\ \\ = \frac{ {11}^{2} - {x}^{2} }{11 - x} \\ \\ = \frac{(11 + x)(11 - x)}{11 - x} \\ \\ = (11 + x) \: m[/tex]

Answer:

on edge

Step-by-step explanation:

The tree increased in height each month until the time period between month 9 and month 11

The statement that can be supported by the given information is, "The height of the tree increased in height each month until the time period between month 9 and month 11".

Given a table that shows the height of the tree that Margo planted over an 11-month period.

When the months are 1, 3, 5, 7, 9, and 11, the height of the tree is 1.4, 1.5, 2.1, 2.7, 3, and 1.8 respectively.

It is clear that the height of the tree increases during the months from 1 to 9.

During the time period between 9 and 11, the height of the tree decreases to 1.8 from 3.

So, the height of the tree increased in height each month until the time period between month 9 and month 11.

Hence the correct option is c.

Learn more about Table Interpretation here :

https://brainly.com/question/32499877

#SPJ7

Answer:

0

Step-by-step explanation:

This is because any number that is plugged in is going to be multiplied by 0. Anything multiplied by 0 is 0. Lastly, 0-0=0, which brings you to your final answer.

Answer:

85 units^2 = Area of Blue Square

and

x = 5 units

Step-by-step explanation:

To do this we use the Pythagorean theorem (a^2 + b^2 = c^2). a and b represent the legs of the triangle whereas c represents the longest side of the triangle, or the hypotenuse.

Since we know the area of a square is the side length multiplied by itself (or the side length squared), [tex]\sqrt{35}[/tex] is the side length of the pink square and [tex]\sqrt{50}[/tex] is the side length of the green square.

That means a = [tex]\sqrt{35}[/tex] and b = [tex]\sqrt{50}[/tex] , so...

[tex](\sqrt{35} )^{2} + (\sqrt{50})^{2} = c^{2}[/tex]

35 + 50 = c^2

85 = c^2

[tex]\sqrt{85} = c[/tex]

Now we need to square the square root of 85 to find the area of the blue square.

[tex](\sqrt{85})^{2} = Area of blue square[/tex]

85 units^2 = Area of Blue Square

To solve the other question we use the same formula again.

[tex]x^2 + 12^2 = 13^2\\x^2 +144 = 169\\-144\\x^2 = 25\\x=\sqrt{25} \\x=5[/tex]

x = 5 units

Notice that

[tex]\left(x-\dfrac1x\right)^2=x^2-2+\dfrac1{x^2}=18-2=16[/tex]

which tells us

[tex]x-\dfrac1x=\pm4[/tex]