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2 years ago

Frank wants to build a garden with the dimensions below.

Mathematics

2 answers:

dexar [7]2 years ago

7 0

Given:
Length = x + x + 3 = 2x + 3
Width = 2 + x

Area = length * width
91 ft² = (2x + 3) (2+x)
91 = 4x + 2x² + 6 + 3x
0 = 2x² + 7x + 6 - 91
0 = 2x² + 7x - 85

(2x + 17) ( x - 5)

x = -17/2 or x = 5

Let x = 5 ;

length = 2x + 3 = 2(5) + 3 = 13
width = 2 + x = 2 + 5 = 7

Area = 13 x 7 = 91

Perimeter = 2(length + width)
Perimeter = 2(13 + 7)
Perimeter = 2(20)
Perimeter = 20 feet of fencing

lozanna [386]2 years ago

7 0

Answer:

The length is 13 and the width is 7, but the length of fencing, is 40, because there are 4 sides. Two thirteens = 26 + Two sevens = 14

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Determine if the statement is true or false:

erma4kov [3.2K]

Answer:

Step-by-step explanation:

given are four statements and we have to find whether true or false.

.1 If two matrices are equivalent, then one can be transformed into the other with a sequence of elementary row operations.

True

2.Different sequences of row operations can lead to different echelon forms for the same matrix.

True in whatever way we do the reduced form would be equivalent matrices

3.Different sequences of row operations can lead to different reduced echelon forms for the same matrix.

False the resulting matrices would be equivalent.

4.If a linear system has four equations and seven variables, then it must have infinitely many solutions.

True, because variables are more than equations. So parametric solutions infinite only is possible

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2 years ago

PLS HELP ASAP I WILL IVE BRAINLIST ANSWER!!!!!Leon verified that the side lengths 21, 28, 35 form a Pythagorean triple using thi

Juliette [100K]

Answer:

Leon is correct. (Option 1)

Step-by-step explanation:

Given that Leon verified that the side lengths 21, 28, 35 form a Pythagorean triple using this procedure.

Step 1: Find the greatest common factor of the given lengths: 7

Step 2: Divide the given lengths by the greatest common factor: 3, 4, 5

Step 3: Verify that the lengths found in step 2 form a Pythagorean triple.

we have to explain whether or not Leon is correct.

As, 3,4,5 forms a Pythagorean triplet i.e satisfies the Pythagoras theorem

$Hypotenuse^2=Base^2+Perpendicular^2$

⇒ $5^2=3^2+4^2$

Let a, b, c forms a Pythagorean triplet

$a^2+b^2=c^2$

Multiplied by 4 on both sides

⇒ $4a^2+4b^2=4c^2$

⇒ ${2a}^2+{2b}^2={2c}^2$

Hence, we say 4a, 4b and 4c also forms a Pythagorean triplet.

∴ multiplying every length of a Pythagorean triple by the same whole number results in a Pythagorean triple.

Hence, Leon is correct.

4 0

2 years ago

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A statue is mounted on top of a 16 foot hill. From the base of the hill to where you are standing is 77 feet and the statue subt

DanielleElmas [232]

Consider right triangle with vertices B - base of the hill, S - top of the statue and Y - you. In this triangle angle B is right and angle Y is 13.2°. If h is a height of the statue, then the legs YB and BS have lengths 77 ft and 16+h ft.

You have lengths of two legs and measure of one acute angle, then you can use tangent to find h:

$\tan 13.2^{\circ}=\dfrac{\text{opposite leg}}{\text{adjacent leg}} =\dfrac{16+h}{77}, \\ \\ 0.2345=\dfrac{16+h}{77},\\ \\ 16+h=0.2345\cdot 77=18.0565,\\ h=18.0565-16=2.0565$ ft.

Answer: the height of the statue is 2.0565 ft.

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2 years ago

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Allen is showing his work in simplifying –8.3 + 9.2 – 4.4 + 3.7. Identify and explain any errors in his work or in his reasoning

avanturin [10]

Simplifying –8.3 + 9.2 – 4.4 + 3.7.

Identify and explain any errors in his work or in his reasoning

Original problem 1. −8.3 + 9.2 + 4.4 + 3.7

Additive inverse 2. −8.3 + 4.4 + 9.2 + 3.7 (error, not additive inverse; +3-3=0)

Commutative property 3. −8.3 + (4.4 + 9.2 + 3.7)

Associative property 4. −8.3 + 17.3

Simplify 5. 9

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2 years ago

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Marley drives to work every day and passes two independently operated traffic lights. The probability that both lights are red i

madam [21]

Let event A be the first light being red.
Let event B be the second light being red.

P(A) = 0.48
P(A & B) = P(A) * P(B) = 0.35

P(B) = 0.35 / P(A)
P(B) = 0.35 / 0.48
P(B) = 0.73

Since the lights are independent, P(B|A) = P(B) therefore d is the correct answer.

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2 years ago

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