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3 years ago

Need help with question 4

Mathematics

1 answer:

Katarina [22]3 years ago

6 0

9514 1404 393

Answer:

16/7

Step-by-step explanation:

If the segments are congruent, their lengths are equal:

(1/2)x -3 = 5 -3x

(3 1/2)x = 8

x = 8/(3.5) = 16/7

The value of x is 16/7.

_____

Comment on the question

This value of x makes the lengths of the segments be -13/7 units. Usually, negative lengths are considered impossible for line segments.

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Can someone help me with this?

Marianna [84]

Look at the rectangle. The bottom side measures 8 miles, so the top side also measures 8 miles.

Now look at the upper right triangle. For the angle of 32 deg, the top side of the triangle is the adjacent leg of the triangle. The air distance, marked x, is the hypotenuse of the triangle.

The trig ratio that relates the adjacent leg and the hypotenuse is the cosine.

$\cos \theta = \dfrac{adj}{hyp}$

$\cos 32^\circ = \dfrac{8~miles}{x}$

$x = \dfrac{8~miles}{\cos 32^\circ}$

$x = 9.4 ~miles$

6 0

3 years ago

For a certain automobile,

emmasim [6.3K]

Answer:

The answer is

a) 2,128 miles per gallon at 40,36 miles per hour

b) 1,388 miles per gallon at 60 miles per hour

Step-by-step explanation:

Let's find the extreme points of M(x) for 30≤x≤60. M(x) simplified by dividing to 7.8.

$M(x) = -1,92.10^-3x^2+0,155x-1$

To find extreme points we find tangent of M(x) and equal it to 0.

$M'(x) = -3,84.10^-3x+0,155=0$

therefore x= $\frac{-0,155}{-3,84.10^-^3} = 40,36$

This divides our x to 2 different range 30≤x≤40,36 and 40,36≤x≤60

Now we pick a number and investigate from the ranges

30≤x≤40,36 → x = 35 → M'(35) = 0,0206 which is > 0 and that means M is increasing

40,36≤x≤60 → x = 45 → M'(45) = -0,0178 which is < 0 and that means M is decreasing

Next let's look at critical points

x M(x) Before After Decision

30 1,922 - ↑ Local Minimum Point

40,36 2,128 ↑ ↓ Local Maximum Point

60 1,388 ↓ - Local Minimum Point

As we can see (30, 1,922) and (60, 1,388) are local minimum points and (40,36 , 2,128) is the local maximum point.

Since (60 , 1,388) is the lowest local minimum point it is the absolute minimum point and (40,36 , 2,128) is the absolute maximum point.

6 0

3 years ago

What scale factor was applied to the first rectangle to get the resulting image?

Valentin [98]

Answer:

Divided by 5.

Step-by-step explanation:

It is five times smaller than the original picture.

3 0

3 years ago

Miss Holloway has four bags of miniature candy bars. Each bag contains 30 candy bars. How many candy bars with each of the 27 st

Harman [31]

Answer:

four, 12 will be left

Step-by-step explanation:

120/27 equals 4; the remainder (“left over”) is 12

3 0

2 years ago

Read 2 more answers

What's substitution for y=4x-1;y=2x-5

Makovka662 [10]

y=4x−1;y=2x−5
Step: Solve y=4x−1 for y:
Step: Substitute 4x−1 for y in y=2x−5:
y=2x−5
4x−1=2x−5
4x−1+−2x=2x−5+−2x(Add -2x to both sides)
2x−1=−5
2x−1+1=−5+1(Add 1 to both sides)
2x=−4
2x/2=−4/2(Divide both sides by 2)
x=−2
Step: Substitute−2 for x in y=4x−1:
y=4x−1
y=(4)(−2)−1
y=−9(Simplify both sides of the equation)
Answer:y=−9 and x=−2

3 0

3 years ago