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3 years ago

Which function below is the inverse of f(x)=7x-1/2

Mathematics

1 answer:

Margaret [11]3 years ago

5 0

We write f(x) in terms of y I.e y=7x-1/2.

Fractions are sometimes ambiguous, we eliminate the fraction by multiplaying the entire function by 2.so as to get 2y=14x-1.

Make x the subject, x=2y+1/14,

Thus the inverse f(x)=2x+1/14

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The scale of this map is 1 inch = 50 miles. The ruler measures the distance between Gary, Indiana, and Traverse City, Michigan,

levacccp [35]

Answer:

<em>150 miles</em>

Step-by-step explanation:

Given the scale on the map using the conversion factor

1 inch = 50 miles

We are to find the equivalent miles between the cities in miles if the distace is 3inches

3inches = x

Divide both expressions

1/3 = 50/x

Cross multiply

x = 3 * 50

x = 150

<em>Hence the actual distance between these two cities in miles is 150 miles </em>

6 0

3 years ago

Do number 4 please DONT get it wrong or i block report, i really need help please :)

andriy [413]

Area of the figure = 30.28 m²

Solution:

The given image is splitted into two shapes.

One is rectangle and the other is semi-circle.

Length of the rectangle = 6 m

Width of the rectangle = 4 m

Area of the rectangle = length × width

= 6 m × 4 m

= 24 m²

Area of the rectangle = 24 m²

Diameter of the semi-circle = 4 m

Radius of the semi-circle = 4 m ÷ 2 = 2 m

Area of the semi-circle = $\frac{1}{2} \ \pi r^2$

$$=\frac{1}{2} \times 3 .14 \times 2^2$

$=6.28$

Area of the semi-circle = 6.28 m²

Area of the figure = Area of the rectangle + Area of the semi-circle

= 24 m² + 6.28 m²

= 30.28 m²

Area of the figure = 30.28 m²

3 0

3 years ago

4x² = 32 What does x equal

babymother [125]

So here is what you would do:

lets just pretend that there is no x in the equation

so this is what the equation would look like:

first, is 4 to the power of 2=16 and now we are going to put the x back into the equation so: 4x to the power of 2, but we did the exponents so, now x is the missing number. We can use the 32 because it is the solution to the equation. So we would do 32-16=16 so the missing number is 16 so x=16

Answer: x=16

4 0

3 years ago

A rhombus ABCD has AB = 10 and m∠A = 60°. Find the lengths of the diagonals of ABCD.

melisa1 [442]

Three important properties of the diagonals of a rhombus that we need for this problem are:
1. the diagonals of a rhombus bisect each other
2. the diagonals form two perpendicular lines
3. the diagonals bisect the angles of the rhombus

First, we can let O be the point where the two diagonals intersect (as shown in the attached image). Using the properties listed above, we can conclude that ∠AOB is equal to 90° and ∠BAO = 60/2 = 30°.

Since a triangle's interior angles have a sum of 180°, then we have ∠ABO = 180 - 90 - 30 = 60°. This shows that the ΔAOB is a 30-60-90 triangle.

For a 30-60-90 triangle, the ratio of the sides facing the corresponding anges is 1:√3:2. So, since we know that AB = 10, we can compute for the rest of the sides.

$\overline{OB}:\overline{AB} = 1:2$
$\overline {OB}:10 = 1:2$
$\overline{OB} = \frac{1}{2}(10) = 5$

Similarly, we have

$\overline{AO}:\overline{AB} = \sqrt{3}:2$
$\overline {AO}:10 = \sqrt{3}:2$
$\overline{AO} = \frac{\sqrt{3}}{2}(10) = 5\sqrt{3}$

Now, to find the lengths of the diagonals,

$\overline{AD} = 2(\overline{AO}) = 10\sqrt{3}$
$\overline{BC} = 2(\overline{OB}) = 10$

So, the lengths of the diagonals are 10 and 10√3.

Answer: 10 and 10√3 units

8 0

3 years ago

Can someone please help on this problem and how it is done? Picture is attached. Thank you

Vikki [24]

The angle passes 90 degrees plus an additional 55 degrees
m

5 0

3 years ago