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Ira Lisetskai [31]

4 years ago

9

If the vertex of f(x) is (0,3), what is the vertex for 3×f(x-2)? Explain please.

2 answers:

katen-ka-za [31]4 years ago

8 0

Vertex of $3f(x-2)$ is $(0-2,3\cdot3)=(-2,9)$

Kruka [31]4 years ago

6 0

Vertex of 3f(x-2) is (0-2,3\cdot3)=(-2,9) Hope This Helps :))

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Please help me<br><br><br> Simplify.<br><br> 3(x + 4)

valentinak56 [21]

Distribute the 3.

3*x + 3*4
3x + 12

Hope this helps :)

8 0

3 years ago

A rectangular box with a square base is to be constructed from material that costs $9 per ft2 for the bottom, $5 per ft2 for the

kramer

Answer:

$18.73ft^3$

Step-by-step explanation:

Let

Side of square base=x

Height of rectangular box=y

Area of square base=Area of top= $(side)^2=x^2$

Area of one side face= $l\times b=xy$

Cost of bottom=$9 per square ft

Cost of top=$5 square ft

Cost of sides=$4 per square ft

Total cost=$204

Volume of rectangular box= $V=lbh=x^2y$

Total cost= $9(x^2)+5x^2+4(4xy)=14x^2+16xy$

$204=14x^2+16xy$

$204-14x^2=16xy$

$y=\frac{204-14x^2}{16x}=\frac{102-7x^2}{8x}$

Substitute the values of y

$V(x)=x^2\times \frac{102-7x^2}{8x}=\frac{1}{8}(102x-7x^3)$

Differentiate w.r.t x

$V'(x)=\frac{1}{8}(102-21x^2)=0$

$V'(x)=0$

$\frac{1}{8}(102-21x^2)=0$

$102-21x^2=0$

$102=21x^2$

$x^2=\frac{102}{21}=4.85$

$x=\sqrt{4.85}=2.2$

It takes positive because side length cannot be negative.

Again differentiate w.r. t x

$V''(x)=\frac{1}{8}(-42x)$

Substitute the value

$V''(2.2)=-\frac{42}{8}(2.2)=-11.55$

Hence, the volume of box is maximum at x=2.2 ft

Substitute the value of x

$y=\frac{102-7(2.2)^2}{8(2.2)}=3.87 ft$

Greatest volume of box= $x^2y=(2.2)^2\times 3.87=18.73 ft^3$

5 0

4 years ago

The pentagonal prism has a perpendicular distance of 14 units between the bases. The volume of the prism is 840 cubic units. Wha

Leno4ka [110]

Answer:

Option 4. Perimeter = 30 units

Step-by-step explanation:

Since the volume of a pentagonal prism is 840 cubic units.

Perpendicular distance between the bases = 14 units

We know volume of a pentagonal prism = Area of base × distance between the bases

840 = Area × 14

Area = 840/14 = 60 square units

Now area of a pentagon

$A=\frac{a^{2}}{4}\times\sqrt{5(5+2\sqrt{5})}$

$1.72a^{2}=60$

$a^{2}=\frac{60}{1.72}=34.90$

$a=\sqrt{34.9}=5.91$

Therefore perimeter of the pentagon = 5×a = 5×5.91 = 29.54 ≈ 30 units

8 0

3 years ago

Ratio of 9 maple trees to 5 oak trees <br><br> how did they come up with 36 maple trees

miss Akunina [59]

(9×5) - 9 = 36 Maple trees

5 0

3 years ago

How do I solve this and answer?

kodGreya [7K]

Step-by-step explanation:

at first solve first triangle with Pythagorean solving witch it c²=a²+b²

you have to change a bit so it will be c²-b²=a²

you start with 8 and 10 triangle and then you get line which is in the middle and yo udo just the same with triangle 8 and the solved side and you get x in the second triangle you have to use c²-a²=b²

6 0

3 years ago