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Mariulka [41]
3 years ago
9

the wades are putting a 4 inch wallpaper border around their rectangular living room. what are the dimensions of the room if the

width is 3.5 feet less than the length, and the perimeter of the room is 67 feet.
Mathematics
1 answer:
Ludmilka [50]3 years ago
6 0
Let x be the width of the room. I<span>f the width is 3.5 feet less than the length, then the length is x+3.5. The perimeter is x+x+x+3.5+x+3.5=4x+7.
</span>
Since the perimeter is equal to 67, then 4x+7=67, 4x=60, x=60÷4, x=15 ft and x+3.5=15+3.5=18.5 ft.
Answer: the width is 15 ft, the length is 18.5 ft.
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Given f(x) = 4(1 – x), what is the value of f(-10)
Lubov Fominskaja [6]

Answer:

44

Step-by-step explanation:

The function formula is given as

f(x) = 4(1 – x)

To find the f(-10) we will substitute into the function formula, then we have

f(-10)= 4[1-(-10)]

=4[11]

=44

Hence, the value of f(-10)= 44

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Find the value of x given the figure below.
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Here’s the step-by-step answer!

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A rabbit and a turtle were to start a race at the same place. The rabbit was asleep when the turtle started. He slept for seven
Ierofanga [76]
Rabbit: y=5x-7
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3 years ago
Consider the equations y = 3x and y = -12- x.
jasenka [17]

Answer:

x | -7      -5     -3  

y | -21    -15    -9

Step-by-step explanation:

y = 3x

If x = -7  then y = 3 × (-7) = -21

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5 0
2 years ago
1 The prism-shaped roof has equilateral triangular bases. Use the model you created in question #1 to calculate the height of th
Diano4ka-milaya [45]

Answer:

Step-by-step explanation:

Step-by-step explanation:  As shown in the attached figure, the prism-shaped roof has equilateral triangular bases, one of which is ΔABC. We need to create an equation that models the height of one of the roof's triangular bases in terms of its sides. Let ii be AD.

See the figure attached herewith, ΔABC forms an equilateral triangle, in which AD is the height. So, D will be the mid-point of BC and ∠ADB = ∠ADC = 90°.

Now, in ΔADB, we have

AD^2=AB^2-BD^2

AD^2=AB^2-(1/2AB^2)^2

AD=√3/4AB^2

we can find the height of any one of the roof's triangular bases.

2.1. Check picture 1. Let the one side of the triangle be a, drop one perpendicular, CD. Then triangle ADB is a right triangle, with hypothenuse a and one side equal to 1/2a. By the Pythagorean theorem, as shown in the picture, the height is √3/2a

2. if a=25 ft, then the height is  √3/2a=√3/2*25=1.732/2*25=21.7(ft)

3. consider picture 2. Let the length of the roof be l feet.

one side of the prism (the roof) is a rectangle with dimensions a and l, so the area of one side is a*l

the lateral Area of the roof is 3a*l

the area of the equilateral surfaces is 2*(1/2*a*√3/2a)=√3/2a^2  

so the total area of the roof is  

4. The total area was the 2 triangular surfaces + the 3 equal lateral rectangular surfaces. Now instead of 3 lateral triangular surfaces, we have 2.

So the total area found previously will be decreased by al

5. so the area now is √3/2a^2 + 2al  

6. now a=25 and l=2a=50

Area= √3/2a^2+2al=√3/2*25^2+2*25*50=25^2(√3/2+4)=625*4.866

=3041.3 (ft squared)

6 0
3 years ago
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