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timama
1 day ago
12

A giraffe measures 17 feet tall . A gorilla mesures 63 inches tall. How many feet taller is the giraffe than the gorilla

Mathematics
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Angela makes a pillow in the shape of a wedge to use for watching TV. The pillow is filled with 0.35 m3 of fluffy
Svet_ta [12734]

Complete Question

Angela has constructed a wedge-shaped pillow for her TV watching needs. It contains 0.35 m³ of fluffy material. The pillow's base area measures 0.5m², and its height stands at 1m.

What is the length of the pillow?

Provide an exact answer (no rounding).

Answer:

1.4m

Step-by-step explanation:

A wedge can be defined as a Triangular prism. Thus,

The volume formula for a wedge (Triangular prism) is given by: 1/2 × B × H × L

b = 0.5m

h = 1 m

l =??

Volume of the wedge = 0.35 m³

0.35 = 1/2 × 0.5 × 1 × L

0.35 = 0.25 × L

Solving for L, we get: L = 0.35/0.25

L = 1.4m

4 0
3 months ago
Chris has a cell phone plan with a flat fee of $26.00 per month, plus a cost of $0.12 per minute of usage. Chris can only afford
tester [12383]

For Chris, the calculation for his monthly telephone expense is as follows:

C (x) = 26 + 0.12x

Where "x" denotes each minute used.

Given that Chris can afford a bill of $86, we have:

26 + 0.12x \leq86\\0.12x \leq86-26\\0.12x \leq60\\x \leq \frac {60} {0.12}\\x \leq500

The total minutes of usage must not exceed 500 per month. Consequently, the viable choice is option C.

Answer:

Option C

3 0
3 months ago
The length and width of a book cover are 22.2cm and 12 cm respectively
zzz [12365]

The dimensions of the book cover are 28.3 centimeters in length and 21 centimeters in width. Calculate the range of values for both the actual length and width of the book cover. Minimum length = (28.3 - 0.05) cm and maximum length = (28.3 + 0.05) cm, thus 28.25 cm ≤ length < 28.35 cm.

Hope this information is helpful!

8 0
2 months ago
Two functions are shown in the table below. Function 1 2 3 4 5 6 f(x) = −x2 + 4x + 12 g(x) = −x + 6 Complete the table on your o
Svet_ta [12734]

For \fbox{\begin \\\math{x}=6\\\end{minispace}} the function f(x)=-x^{2} +4x+12 and g(x)=-x+6 both yield the same result.

Detailed breakdown:  

The functions involved are

f(x)=-x^{2}+4x+12

g(x)=-x+6

Step 1:  

Insert x=1 in f(x)=-x^{2} +4x+12 to find the value of f(1).

f(1)=-1^{2} +4(1)+12\\f(1)=-1+4+12\\f(1)=15

Insert x=1 in g(x)=-x+6 to find the value of g(1).

g(1)=-1+6\\g(1)=5

Step 2:

Insert x=2 in f(x)=-x^{2} +4x+12 to obtain the value of f(2).

f(2)=-2^{2} +4(2)+12\\f(2)=-4+8+12\\f(2)=16

Substitute x=2 into g(x)=-x+6 to find the value of g(2).

g(2)=-2+6\\g(2)=4

Step 3:

Replace x=3 in f(x)=-x^{2} +4x+12 to find the value of f(3).

f(3)=-3^{2} +4(3)+12\\f(3)=-9+12+12\\f(3)=15

Also, replace x=3 in g(x)=-x+6 to find the value of g(3).

g(3)=-3+6\\g(3)=3

Step 4:

Insert x=4 in f(x)=-x^{2} +4x+12 to find the value of f(4).

f(4)=-4^{2} +4(4)+12\\f(4)=-16+16+12\\f(4)=12

Also, replace x=4 in g(x)=-x+6 to obtain the value of g(4).

g(4)=-4+6\\g(4)=2

Step 5:

Insert x=5 in f(x)=-x^{2} +4x+12 to obtain the value of f(5).

f(5)=-5^{2} +4(5)+12\\f(5)=-25+20+12\\f(5)=7

Replace x=5 in g(x)=-x+6 to find the value of g(5).

g(5)=-5+6\\g(5)=1

Step 6:

Insert x=6 into f(x)=-x^{2} +4x+12 to find the value of f(6).

f(6)=-6^{2} +4(6)+12\\f(6)=-36+24+12\\f(6)=0

Also, substitute x=6 in g(x)=-x+6 to obtain the value of g(6).

g(6)=-6+6\\g(6)=0

Step 7:

According to the provided condition f(x)=g(x).

(a). Insert f(x)=-x^{2} +4x+12 and g(x)=-x+6 into the previously mentioned equation.

-x^{2} +4x+12=-x+6

(b). Multiply through by -1 on both sides.

x^{2} -4x-12=x-6

(c). Move the term x-6 to the left side of the equation.

x^{2} -4x-12-x+6=0\\x^{2} -5x-6=0

(d). Divide the middle term so that its sum equals 5 and the product equals 6.

x^{2} -(6-1)x-6=0\\x^{2} -6x+x-6=0\\x(x-6)+1(x-6)=0\\(x+1)(x-6)=0\\x=-1,6

From the analysis above, it is noted that for x=6 both functions f(x) and g(x) yield the same outcome.

Using a direct approach:

f(x)=g(x)\\\Leftrightarrow-x^{2} +4x+12=-x+6\\\Leftrightarrow-x^{2} +4x+12+x-6=0\\\Leftrightarrow-x^{2} +5x+6=0\\\Leftrightarrow-x^{2} +6x-x+6=0\\\Leftrightarrow x^{2} -6x+x-6=0\\\Leftrightarrow x(x-6)+1(x-6)=0\\\Leftrightarrow(x+1)(x-6)=0\\\Leftrightarrow x=6,-1

The table representing function f(x)=-x^{2} +4x+12 and g(x)=-x+6 is included below.

For more information:

1. What is the y-intercept of the quadratic function f(x) = (x – 6)(x – 2)? (0,–6) (0,12) (–8,0) (2,0)

2. Which is the graph of f(x) = (x – 1)(x + 4)?

6 0
2 months ago
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