Vanessa uses the expressions (3x2 + 5x + 10) and (x2 – 3x – 1) to represent the length and width of her patio. Which expression represents the area (lw) of Vanessa’s patio?

Answer:

The height is 12 cm

Step-by-step explanation:

Hi there!

We are given a triangle with the 3 sides marked as 15, 20, and 25 and we want to find the height of it (marked as x in the problem).

This problem can seem a bit difficult, but let's see if the triangle is a right triangle first off.  

One way to figure out if it is a right triangle is to apply the converse of the Pythagorean theorem.

Let's label the sides, where a is the shortest side, b is the second shortest side, and c is the longest side:

a=15

b=20

c=25  

Now square a and b, then add the result together. If it's the same as c squared, then the triangle is a right triangle

15²+20²=25²

225+400=625

625=625

So we can safely say that the triangle is a right triangle

This makes the problem way easier, as there are 2 ways to find the area of a right triangle:

The first way is to multiply the legs (the sides that make up the right angle) together, then divide the result by 2

The other way is to multiply the height and the hypotenuse (the side OPPOSITE to the right angle) together, and then divide the result by 2

First, we need to figure out which sides are the legs, and which side is the hypotenuse

By the triangle inequality theorem, the hypotenuse of a right triangle is the longest side, which means that the 25 cm side is the hypotenuse, and that leaves 15 cm and the 20 cm sides as the legs

So let's find the area of the triangle using the legs

A=[tex]\frac{15*20}{2}[/tex]=[tex]\frac{300}{2}[/tex]=150

So the area of the triangle is 150 cm²

However, as mentioned above, we can also find the area of the triangle by multiplying the hypotenuse by the base, then dividing the result by 2

Which means that the area is also:

A=[tex]\frac{25x}{2}[/tex] cm²

As these both equal the area of the triangle, we can set them equal to each other. This is possible via a property known as transitivity (if a=b and b=c, then a=c)

[tex]\frac{25x}{2}=150[/tex]

Multiply both sides by 2

25x=300

Divide both sides by 25

x=12 cm

So the height of the triangle is 12 cm

Hope this helps!

Answer:

Step-by-step explanation:

0.6821 multiplied by 0.0261 is .01754181

putting that into standard from would be 1.754181 x 10^-2

Answer:

The correct option is;

Formal

Step-by-step explanation:

The common levels of diction are formal, informal, and popular, with formal diction being the most selective of the word choices

Formal diction is used when when communicating in a situation that is formal

Formal diction uses languages that is devoid of slang and grammatically correct

Formal language is precise, grammatically correct language that does not use slang used in communication for legal, professional, business and academic purposes.

Answer:

I hope it helps.

The solutions in photo ^_^

3×4·20 equals to 12.6 please thats youre awnser

Answer:

The ratios are equivalent.  

The ratios are a proportion.

Step-by-step explanation:

Answer:

The digits arranged in order from least to largest is 3.011, 3.09, 3.9, 9.3

Step-by-step explanation:

The arrangement of decimals in order from smallest to largest can be done by  taking note of the  digit in the unit portion, the tenths, hundredths and thousandths.

The numbers are;

9.3

3.09

3.9

3.011

The largest number is the 9.3

Of the three numbers with 3 as unit, the lowest hundredths is 0.011, therefore, we have;

Therefore, the least (lowest) number = 3.011

The next is the 3.09 as 0.09 is larger than 0.011

Then the second number is 3.9

The digits arranged in order from least to largest is then 3.011, 3.09, 3.9, 9.3.

Answer:

D: k*x=y

Step-by-step explanation:

a proportional relationship is basically a linear equation (y=mx+b)

Answer:

6 and 7

Step-by-step explanation:

Answer:

Consecutive terms are numbers which follow each other in order, without gaps, from smallest to largest.

Example:

12, 13, 14 and 15

or

2, 24, 26, 28 and 30 (Even Consecutive)

or

40, 45, 50 and 55 (Consecutive Multiples of 5)

SOURCE/GOOGLE

Answer:

Consecutive numbers are numbers that follows one other in their counting order. Each number in the order will be higher than the previous number by 1.

They are always ordered from the smallest to the largest value.

Step-by-step explanation:

Example :

7, 8, 9, 10 are consecutive numbers.

23, 24, 28, 29 are not consecutive numbers.

Answer:

Step-by-step explanation:

The distance between two points can be found by using the formula

where

(x1 , y1) and (x2 , y2) are the points

From the question , the points are

A(13, 2) and B(7, 10)

The distance between them is

We have the final answer as

Hope this helps you

i hope this helppppsss

Answer:

That is the graph for y = -|x| + 3

Step-by-step explanation:

Soln

Given

Cp of 1 glass tumbler=80.1000

=Rs 80000

Number of broken glass tumbler=50

Number of remaining glass tumbler=1000-50

=950

Sp of one glass tumbler=96

Sp of 950 glass tumbler=96.950

=91200

Now

Sp > Cp so it is profit

Profit%=sp-cp/cp.100

=91200-80000/80000.100

=11200/80000.100

=14%

Answer:

14%profit

Step-by-step explanation:

Cost of 1000 tumblers=1000×80=80,000

50 of them were broken: 1000-50=950

: He sells 950 tumblers of rs.96 each= ( 950×96)

S.P=91200

We can clearly see he gains for rs.11200.

P%=gain/C.P×100

11200×80000×100

=14%

Answer:

-15

Step-by-step explanation:

We proceed as follows;

In this question, we want to fill in the blank so that we can have the resulting expression expressed as the product of two different linear expressions.

Now, what to do here is that, when we factor the first two expressions, we need the same kind of expression to be present in the second bracket.

Thus, we have;

2a(b-3) + 5b + _

Now, putting -15 will give us the same expression in the first bracket and this gives us the following;

2a(b-3) + 5b-15

2a(b-3) + 5(b-3)

So we can have ; (2a+5)(b-3)

Hence the constant used is -15

Answer:

Question 1.

Option A: 2m

Question 2

Option D: (1, 1) minimum point

Step-by-step explanation:

Question 1.

Let the original length of the garden (before expansion) be = x

The new length of the garden will be x + 10m

Recall that the garden has a square geometry. That means that its area is obtained by squaring any of its sides.

This means that [tex](x +10)^2 = 144[/tex]

We can now solve for x

[tex](x +10)^2 = 144\\x^2 +20x +100 = 144\\x^2 + 20x =44\\x^2 + 20x - 44=0\\x = 2 or -22[/tex]

x cannot be a negative number, so the original length of a side of the garden is 2m. Option A

Question 2:

The coordinates of the vertex of the graph (turning point) are (x, y) [1,1]

To know whether it is a minimum or maximum point, we will have to check the coefficient of [tex]x^2[/tex] in the equation [tex]y = x^2-2x+2[/tex]

The coefficient of  [tex]x^2[/tex] in the equation is 1. (If no number is present, just know that the coefficient is a one).

If the coefficient is positive, then the point is a minimum point. However, if it is negative, then the point is a maximum point.

Our coefficient is positive hence, the graph has a minimum point.

Answer:

The answer is below

Step-by-step explanation:

To find the maximum amount of cargo the truck can carry, we need to find the volume of the truck.

Volume = length × width × height.

Firstly 1 feet (1') = 12 inches (12"),

For the extra ledge that sticks out, the height = 7'8" = 7.667 feet, the width = 16'9" - 14'3" = 16.75 - 14.25 = 2.5 feet, the length = 2'7" = 2.583 feet

Volume of extra ledge = length × width × height = 2.583 × 2.5 × 7.667 = 49.5 feet³

For the truck, the height = 7'8" = 7.667 feet, the length = 14'3" = 14.25 feet, the width = 6'6" = 6.5 feet

Volume of truck = length × width × height = 14.25 × 6.5 × 7.667 = 710.16 feet³

The maximum volume = volume of extra ledge + volume of truck = 49.5 + 710.16 = 759.66 feet³

Answer:

C = 16pi or ≈50.24 units

Step-by-step explanation:

(x − 9)^2 + (y − 3)^2 = 64

This equation is in the form

(x-h)^2 + (y-k)^2 = r^2

The radius is 8

The circumference is given by

C = 2*pi*r

C = 2*pi*8

C = 16 pi

Using 3.14 as an approximation for pi

C = 16(3.14)

C ≈50.24

Answer:

12x⁴ - 15x³ + 18x²

Step-by-step explanation:

1. distribute -3x²

-3x² • 5x = -15x³

-3x² • -4x² = 12x⁴

-3x² • -6 = 18x²

2. combine terms and put in descending order (standard form)

12x⁴ - 15x³ + 18x²

Answer:

12x⁴ - 15x³ + 18x²

Step-by-step explanation:

1. distribute -3x²

-3x² • 5x = -15x³

-3x² • -4x² = 12x⁴

-3x² • -6 = 18x²

2. combine terms and put in descending order (standard form)

12x⁴ - 15x³ + 18x² correct answer would be this

Answer:

Step-by-step explanation:

we use cosine formula

2×15×10×cos(180-66)=15²+10²-AC²

-300 cos 66=225+100-AC²

AC²=325+300 cos 66

[tex]AC=\sqrt{325+300 cos 66} \approx 21.14 ~m/s[/tex]

The distance from A to C is 21.14. The correct option is A.

Trigonometry is the branch of mathematics which set up a relationship between the sides and angles of right-angle triangles.

Velocity is defined as the ratio of the distance moved by the object at a particular time. The velocity is a vector quantity so it needs both the magnitude and the direction.

Given that the velocity of a train relative to the ground is represented by the distance from A to B in the diagram. The velocity of a ball thrown inside the train at an angle of 66° relative to the train is represented by the distance from B to C.

The distance A to C will be calculated as,

2×15×10×cos(180-66)=15²+10²-AC²

-300 cos 66=225+100-AC²

AC=√(325+300 cos 66)

AC = 21.17 m/s

Therefore, the distance from A to C is 21.14. The correct option is A.

To know more about trigonometry follow

https://brainly.com/question/14931414

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Answer:

16

Step-by-step explanation:

Distribute 7 into x and 2, which gets you 7x+14. Then distribute 6 into x and 5, which is 6x+30. 7x-6x= x, 30-14=16 so there’s your answer.

Answer:

Step-by-step explanation:

7x + 14 = 6x + 30

x + 14 = 30

x = 16

Answer:

Step-by-step explanation:

We know, for square

[tex](side)^2=(Area)\\=>X^2=8\\[/tex]

∴[tex]X=2\sqrt{2}[/tex] unit

[tex]Now, Side=3X[/tex]

[tex]Then,Area=(3X)^2=(3*2\sqrt{2} )^2=(6\sqrt{2} )^2=72 sq. unit[/tex]

hope you have understood this...

pls mark my answer as the brainliest

The area of square of side 3X is 72 square unit.

The square is a 4 sided figure, each side of the square is equal and make a right angle.

The area of square having sided a unit can be given by a² square unit.

Given that,

Area of square having side X is 8.

Since, formula for area of square having side X is X².

Implies that,

X² = 8

X = 2√2

The area of square having side 3X
side =3 × 2√2

side = 6√2

The area of square = (6√2)²

                                = 36 x 2

                                = 72

The area of square is 72 square unit.

To know more about Square on:

https://brainly.com/question/28776767

#SPJ2

Answer:

Step-by-step explanation:

Since the triangle is a right angled triangle we can use Pythagoras theorem to find the missing side x

Using Pythagoras theorem we have

a² = b² + c²

where a is the hypotenuse

From the question x is the hypotenuse

So we have

Find the square root of both sides

We have the final answer as

Hope this helps you

Answer:

2 sqrt(41) =c

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2

8^2 + 10^2 = c^2

64+ 100 = c^2

164 = c^2

take the square root of each side

sqrt(164) = sqrt(c^2)

sqrt(4*41) = c

2 sqrt(41) =c

Answer:5

Step-by-step explanation:30/600×100

Answer:

Step-by-step explanation:

[tex]\frac{30}{600} \times 100\\\\= \frac{3000}{600}\\ \\= 5\%[/tex]

Step-by-step explanation:

see the answer in attached picture

pls mark me as brainliest pls

Answer:

If two machine works together it takes 180 minute to complete 6480 shirts

Step-by-step explanation:

2400 ÷ 150 = 6

So here,

1st machine produces 20 shirts per minutes

let, x=minutes for shirt's production

Now,

(16+20)x=6480

36x=6480

x=6480/36

Therefor, x=180 minutes

Answer:

[tex]\boxed{\sf a) \ 15.9}[/tex]

Step-by-step explanation:

The triangle is a right triangle.

We can use trig functions to solve for x.

cos θ = adj/hyp

cos(51) = 10/x

x = 10/cos(51)

x = 15.89015729

Answer:

P(NOT printed page) = 3/38

Step-by-step explanation:

Total pages = 27+8+3=38

Types of pages that satisfy requirement(s)= 3

Therfore, P(NOT printed page) = 3/38

Answer:

3846.5 in.

Step-by-step explanation:

πr² = (3.14)(35)² = 3846.5 in.

[tex]\\ \sf\longmapsto 256x^2y^2-x^2y^2+49y^2x^2[/tex]

[tex]\\ \sf\longmapsto 256x^2y^2-x^2y^2+49x^2y^2[/tex]

[tex]\\ \sf\longmapsto (256-1+49)x^2y^2[/tex]

[tex]\\ \sf\longmapsto 304x^2y^2[/tex]

Answer:

B

Step-by-step explanation:

The side you have drawn in is 4√3 (calculate via pythagoras as √(8²-4²) = √48 = √16·3 = √4²·3 = 4√3)

So the area of the small triangle is 4*2√3 and the area of the small rectangle is 2*4√3. Together makes 4*2√3 + 2*4√3 =  16√3