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s344n2d4d5 [400]
3 years ago
5

If f(x) = x and g(x) = 2x + 7, what isf[90X)] when g(x) = 11?​

Mathematics
1 answer:
kumpel [21]3 years ago
8 0

\bf \begin{cases} f(x) = x\\ g(x) = 2x+7 \end{cases}~\hspace{7em}g(x)=11\implies \stackrel{g(x)}{11}=2x+7 \\\\\\ 4=2x\implies \cfrac{4}{2}=x\implies \implies \boxed{2=x} \\\\[-0.35em] ~\dotfill\\\\ f[90x]\implies f\left[90\left( \boxed{2} \right)\right]\implies f(180)=\stackrel{x}{180}

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katovenus [111]

Answer:

BM: <u>y = (2/3) x + 16/3</u> with segment length of 2.77

Step-by-step explanation:

AC formula: m = (6-0)/(0-4) = -3/2

(y-0)/(x-4) = -3/2       y = (-3/2)x + 6   ... (1)

BM slope: BM⊥ AC   m = 2/3

BM formula: (y-4) / (x- -2) = (y-4) / (x+2) = 2/3

y-4 = 2/3 x + 4/3

<u>y = (2/3) x + 16/3</u>   ... (2)    -2≤x≤0.31

intercept of AC and BM (M) from (1) and (2): (-3/2)x + 6 = (2/3) x + 16/3

(13/6) x = 2/3      x = (2/3) / (13/6) = 4/13 ≈ 0.31

y = (2/3) (4/13) + (16/3) = (8/39) + (208/39) = 216/39 = 72/13 ≈ 5.54

M (4/13 , 72/13) or (0.31 , 5.54)

segment BM = √(4/13 - -2)² + (72/13 - 4)² = √1300/169 = 2.77

4 0
2 years ago
What is the value of x in the equation below?
sveta [45]

Answer: C

Step-by-step explanation:

1+2e^x+1=9

2e^x+1=9-1

e^x+1= 8/2

e^x+1 = 4

Here we can applicate the Ln:

ln e^x+1 = ln 4

Applicating the log property for exponent:

(x+1).ln e = ln 4

Ln e = 1, so:

x+1 = ln 4

x = ln 4-1

7 0
3 years ago
Find the volume of this triangular prism.
Ivanshal [37]

Answer:

45m^3

Step-by-step explanation:

Given that the area of thee triangle is 3m^2 and the volume formula is b x h x w. You have b x h of the triangle so you just need to multiply by the width of the prism which is 15. 3x15=45

7 0
3 years ago
Write the equation that describes the line with slope = 1 and y-intercept= 5/2 in slope-intercept form.
Nonamiya [84]

Answer: y=x+5/2

Step-by-step explanation:

using the slope intercept formula, y=mx+b where m is the slope and b is the y-intercept, you can substitute the two values to get y=x+5/2. Please note that the slope, m, is one so it's not shown.

3 0
3 years ago
A truck driver travels at 59 miles per hour. The truck tires have a diameter of 30 inches. What is the angular velocity of the w
Misha Larkins [42]

Answer:

661.4\ rpm

Step-by-step explanation:

we know that

1 mile=63,360 inches

step 1

Find the circumference of the wheels

C=2\pi r

we have

r=30/2=15\ in -----> the radius is half the diameter

substitute

C=2\pi(15)

C=30\pi\ in

assume

\pi =3.14

C=30(3.14)=94.2\ in

Remember that    

The circumference of the wheels represent one revolution

Convert 59 miles per hour to inches per minute

59\ mi/h=59*63,360/60=62,304\ in/min

using proportion find the number of revolutions  

\frac{1}{94.2}\frac{rev}{in}=\frac{x}{62,304}\frac{rev}{in}\\ \\x=62,304/94.2\\ \\x=661.4\ rev

therefore

substitute

62,304\ in/min=661.4\ rev/min=661.4\ rpm

5 0
3 years ago
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