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2 years ago

Evaluate |15 - 23 | =

Mathematics

1 answer:

masha68 [24]2 years ago

7 0

Answer:

Step-by-step explanation:

$|15 - 23| = | - 8| = 8$

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Allison has three containers with 25 crayons in each. She also has four boxes of markers with 12 markers in each box. She gets 1

Advocard [28]

25x3=75
4x12=48
48-10=38

75 crayons and 38 markers

3 0

3 years ago

Patrick has just finished building a pen for his new dog. The pen is 3 feet wider than it is long. He also built a doghouse to p

zalisa [80]

General Idea:

(i) Assign variable for the unknown that we need to find

(ii) Sketch a diagram to help us visualize the problem

(iii) Write the mathematical equation representing the description given.

(iv) Solve the equation by substitution method. Solving means finding the values of the variables which will make both the equation TRUE

Applying the concept:

Given: x represents the length of the pen and y represents the area of the doghouse

Statement 1: "The pen is 3 feet wider than it is long"

$Length \; of\; the \; pen = x\\ Width \; of\; the\; pen=x+3$

------

Statement 2: "He also built a doghouse to put in the pen which has a perimeter that is equal to the area of its base"

$Area \; of\; the\; Dog \; house=y\\ Perimeter \; of\; Dog\; house=y$

------

Statement 3: "After putting the doghouse in the pen, he calculates that the dog will have 178 square feet of space to run around inside the pen."

$Area \; of \; the\; Pen - Area \;of \;the\;Dog \;House=\;Space\;inside\;Pen\\ \\ x \cdot (x+3)-y=178\\ Distributing \;x\;in\;the\;left\;side\;of\;the\;equation\\ \\ x^2+3x-y=178\Rightarrow\; 1^{st}\; Equation\\$

------

Statement 4: "The perimeter of the pen is 3 times greater than the perimeter of the doghouse."

$Perimeter\; of\; the\; Pen=3\; \cdot \; Perimeter\; of\; the\; Dog\; House\\ \\ 2(x \; + \; x+3)=3 \cdot y\\ Combine\; like\; terms\; inside\; the\; parenthesis\\ \\ 2(2x+3)=3y\\ Distribute\; 2\; in\; the\; left\; side\; of\; the\; equation\\ \\ 4x+6=3y\\ Subtract \; 6\; and \; 3y\; on\; both\; sides\; of\; the\; equation\\ \\ 4x+6-3y-6=3y-3y-6\\ Combine\; like\; terms\\ \\ 4x-3y=-6 \Rightarrow \; \; 2^{nd}\; Equation\\$

Conclusion:

The systems of equations that can be used to determine the length and width of the pen and the area of the doghouse is given in Option B.

$178=x^2+3x-y\\ \\ -6=4x-3y$

8 0

3 years ago

Read 2 more answers

Write the quadratic equation whose roots are 2 and -4 and whose leading coefficient is 2

Goryan [66]

Answer:

2x^2+4x-16

Step-by-step explanation:

The quadratic can be written as

f(x) = a(x-z1)(x-z2) where z1 and z2 are the roots

f(x) = a (x-2)(x- -4)

a is the leading coefficient

f(x) = 2(x-2)(x+4)

= 2(x^2 -2x+4x-8)

= 2(x^2 +2x-8)

= 2x^2 +4x-16

5 0

3 years ago

How many lines of symmetry does this figure have A 1 B, 2 C. 3 D, 4

defon

Answer:

A.1

Step-by-step explanation:

Trapezoids only have one vertical line of symmetry

6 0

3 years ago

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How to solve x in the equation 9x over 2 - 6=5

drek231 [11]

Step-by-step explanation:

$\frac{9x}{2} - 6 = 5 \\ \\ \therefore \: \frac{9x}{2} = 5 + 6 \\ \\ \therefore \: \frac{9x}{2} = 11 \\ \\ \therefore \: 9x = 11 \times 2 \\ \\ \therefore \: 9x = 22 \\ \\ \therefore \: x = \frac{22}{9} \\ \\ \therefore \: x = 2 \frac{4}{9}$

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3 years ago