All categories

2 years ago

Choose the table that represents g(x) = −2⋅f(x) when f(x) = x + 4

Mathematics

1 answer:

fomenos2 years ago

6 0

Answer:

x g(x)

1 −10

2 −12

3 −14

Step-by-step explanation:

Substitute the values and do the arithmetic.

Table values for x are 1, 2, 3. We only need to find g(1) to determine which table is the correct choice.

f(1) = 1 +4 = 5 . . . . . . . . . put 1 where x is and do the arithmetic

g(1) = -2·f(1) = -2·5 = -10 . . . . . matches the 3rd choice

You might be interested in

What is the complete factorization of 36y2 − 1?

ludmilkaskok [199]

Answer:

36y² - 1

Factorize

We have the final answer as

$(y - \frac{1}{6} )(36y + 6)$

Hope this helps you

3 0

3 years ago

A rectangle is 32m by 8m is similar to a rectangle 4m by x m.

Flauer [41]

Answer:

x = 1

Step-by-step explanation:

x/4 = 8/32

x = 1

Best Regards!

5 0

3 years ago

Read 2 more answers

you have driven the first 150 miles of a 2000 mile trip. ��what percentage of the trip have you traveled?

miskamm [114]

150/2000 cause 2000 would be your bottom number and 150 is your is your top number

8 0

3 years ago

Figure A is a scale image of Figure B.<br> What is the value of x?

Leto [7]

Answer:

The required value of x is 12 units.

Step-by-step explanation:

Given that the figure A is a scale image of figure B.

We are to find the value of x.

Since figure A is the scale image of figure B, so both the figures are similar to each other.

Also, the corresponding sides of the similar figures are proportional, so we get

Thus, the required value of x is 12 units.

5 0

2 years ago

Two different right cones are being considered by a design team to hold one liter (1000

ollegr [7]

Answer:

The surface area of Design A is smaller than the surface area of Design B.

The area of Design A is 94.65% of the Design B.

Step-by-step explanation:

The area of a right cone is given by the sum of the circle area of the base and the lateral area:

$A = \pi r^{2} + \pi rL$ (1)

Where:

r: is the radius

L: is the slant height

The slant height is related to the height and to the radius by Pitagoras:

$L^{2} = H^{2} + r^{2}$

$L = \sqrt{H^{2} + r^{2}}$ (2)

By entering equation (2) into (1) we have:

$A = \pi r^{2} + \pi r(\sqrt{H^{2} + r^{2}})$

Now, let's find the area of the two cases.

Design A: height that is double the diameter of the base, H= 2D = 4r

$A_{1} = \pi r^{2} + \pi r(\sqrt{(4r)^{2} + r^{2}}) = \pi r^{2}(1+ \sqrt{17})$

The volume of the cone is:

$V = \frac{1}{3}\pi r^{2}H$

We can find "r":

$V = \frac{1}{3}\pi r^{2}(4r) = \frac{4}{3}\pi r^{3}$

$r = \sqrt[3]{\frac{3V}{4\pi}} = \sqrt[3]{\frac{3*1000}{4\pi}} = 6.20 cm$

The area is:

$A_{1} = \pi (6.20)^{2}(1+ \sqrt{17}) = 618.7 cm^{2}$

Design B: height that is triple the diameter of the base, H = 3D = 6r

The radius is:

$r = \sqrt[3]{\frac{3V}{6\pi}} = \sqrt[3]{\frac{3*1000}{6\pi}} = 5.42 cm$

The area is:

$A_{2} = \pi r^{2} + \pi r(\sqrt{(6r)^{2} + r^{2}}) = \pi r^{2}(1 + \sqrt{37}) = \pi (5.42)^{2}(1 + \sqrt{37}) = 653.7 cm^{2}$

Hence, the surface area of Design A is smaller than the surface area of Design B.

The percent of the surface area of Design A is less than Design B by:

$\% A = \frac{618.7 cm^{2}}{653.7 cm^{2}}\times 100 = 94.65 \%$

Therefore, the area of Design A is 94.65% of the Design B.

I hope it helps you!

3 0

2 years ago