I’m really struggling with this problem. Answer with step by step solution is highly appreciated

Answer:

[tex]\frac{1}{x^{5} }[/tex]

Step-by-step explanation:

x^-12/ x^-7

= x^(-12-(-7))

= x^-5

= 1/x^5

Answer:

2a+b=0

ac-b=16

a+b/a=-4

8a+5b=-4

-4a-b =4

3c/-5=6

Step-by-step explanation:

g(5)=2(5)-5=5

h(2)=4(2)+5=13

g(5)+h(2)=5+13=18

Step-by-step explanation:

To evaluate such, the following formula is required:

Distance Formula: d(P, Q) = √ (x2 − x1)^2 + (y2 − y1)^2

Denote the following points as the following,

(4, -7). (1, -7)

X1 Y1. X2. Y2

D(P, Q) = √(1 - 4)^2 + (-7 + 7)^2. <== Since there is a double negative, such will be considered addition.

√(-3)^2 + (0)^2

√9 = 3

Thus, the agglomerate distance of such points on the Cartesian plane is disclosed as 3 units.

Recall the definition of absolute value:

• |x| = x if x ≥ 0

• |x| = -x if x < 0

So you need to consider 4 different cases (2 absolute value expressions with 2 possible cases each).

(i) Suppose 2x + 3 < 0 and x - 2 < 0. The first inequality says x < -3/2 and the second says x < 2, so ultimately x < -3/2. Then

|2x + 3| + |x - 2| = 6x

-(2x + 3) - (x - 2) = 6x

-2x - 3 - x + 2 = 6x

-3x - 1 = 6x

9x = -1

x = -1/9

But -1/9 is not smaller than -3/2, so this case provides no valid solution.

(ii) Suppose 2x + 3 ≥ 0 and x - 2 < 0. Then x ≥ -3/2 and x < 2, or -3/2 ≤ x < 2. Under this condition,

|2x + 3| + |x - 2| = 6x

(2x + 3) - (x - 2) = 6x

2x + 3 - x + 2 = 6x

x + 5 = 6x

5x = 5

x = 1

This solution is valid because it does fall in the interval -3/2 ≤ x < 2.

(iii) Suppose 2x + 3 < 0 and x - 2 ≥ 0. Then x < -3/2 or x ≥ 2. So

|2x + 3| + |x - 2| = 6x

-(2x + 3) + (x - 2) = 6x

-2x - 3 + x - 2 = 6x

-x - 5 = 6x

7x = -5

x = -5/7

This isn't a valid solution, because neither -5/7 < -3/2 nor -5/7 ≥ 2 are true.

(iv) Suppose 2x + 3 ≥ 0 and x - 2 ≥ 0. Then x ≥ -3/2 and x ≥ 2, or simply x ≥ 2.

|2x + 3| + |x - 2| = 6x

(2x + 3) + (x - 2) = 6x

2x + 3 + x - 2 = 6x

3x + 1 = 6x

3x = 1

x = 1/3

This is yet another invalid solution since 1/3 is smaller than 2.

So there is one solution at x = 1.

Answer:

  (a)  no solution

Step-by-step explanation:

Writing the second equation in slope-intercept form, it becomes ...

  3x -y = 2 . . . . given

  y = 3x -2 . . . . add y-2 to both sides

The first equation is already in slope-intercept form:

  y = 3x +3 . . . . first equation

The coefficients of x in the two equations are both 3, so the lines they describe are parallel. They do not intersect, so there is no solution.

Answer:

y=3x+9......(i)

y=-4x-12...(ii)

these are the equation

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]3=\frac{a+r}{a-r} \\3a-3r=a+r\\3a-a=r+3r\\4r=2a\\r=\frac{1}{2} a[/tex]

Answer:

5.30

Step-by-step explanation:

Total cost = flat fee + cost per mile * number of miles

              c(m)  = 3.50 + .60m

Let m=3

c(3)  = 3.50 + .60(3)

    = 3.50 + 1.80

    =5.30

Answer:

B: $5.30

Step-by-step explanation:

Each mile is $0.6, to get the result for 3 miles we would need to multiply $0.6 by 3. $0.60 * 3 = $1.8. Finally we would need to add the 3.50 to $1.8 resulting in $5.30

Answer:

[tex]50 N[/tex]

Step-by-step explanation:

To help us find our answer, we need to use Newton's Second law

[tex]F = m \times a[/tex]

Where F is the force (N), m is the mass (Kg) and a is the acceleration (m/s^2, on a planet this would just be the gravity)

So if we know that a person has a mass of 3Kg and weighs 30N, the acceleration (or the gravity on that planet is)

[tex]30 = 3 \times a\\a = 10 m/s^2[/tex]

Now that we know the acceleration we can easily find the weight of the person.

[tex]F = 5 * 10 = 50 N[/tex]

Answer:

Step-by-step explanation:

Arc length of the circle is given by,

Arc length = [tex]\frac{\theta}{360^{\circ}}(2\pi r)[/tex]

Area of the sector of a circle = [tex]\frac{\theta}{360^{\circ}}(2\pi r)[/tex]

22). Arc length of the circle having central angle = [tex]\frac{\pi}{3}[/tex]

                                                                                 = 60°

Arc length = [tex]\frac{60^{\circ}}{360^{\circ}}(2\pi )(7)[/tex]

                 = [tex]\frac{14\pi }{6}[/tex]

                 = 7.33 cm

23). Arc length of the circle having central angle = 225°

Arc length = [tex]\frac{225^{\circ}}{360^{\circ}}(2\pi )(10)[/tex]

                 = 12.5π

                 = 39.27 km

24). Central angle = [tex]\frac{5\pi }{4}[/tex]

                              = [tex]\frac{5\times 180^{\circ}}{4}[/tex]

                              = 225°

Area of the sector = [tex]\frac{225^{\circ}}{360^{\circ}}(2\pi )(11)[/tex]

                               = 43.20 yd²

25). Area of the sector = [tex]\frac{270^{\circ}}{360^{\circ}}(2\pi )(14)[/tex]

                                      = 65.97 yd²

Answer:

no

Step-by-step explanation:

Answer:

See explanation

Step-by-step explanation:

Maximum weight = 20 kg

Bag 1 = 3.5kg

Bag 2 = 15 kg

Bag 3 = 2kg

Bag 4 = 1.5kg

Total weight of bags = 22 kg

Excess weight of his luggage = Total weight of bags - Maximum weight

= 22 kg - 20 kg

= 2 kg

Express the excess weight as a percentage of his maximum weight allowed = excess weight / maximum weight × 100

= 2/20 × 100

= 0.1 × 100

= 10%

Express the excess weight as a percentage of his maximum weight allowed = 10%

Answer:

O I, II, and III only

Step-by-step explanation:

x-3 < 2

Add 3 to each side

x-3+3< 2+5

x<5

-3 is less than 5

0 is less than 5

2 is less than 5

5 is not less than 5

I , II , II are true

Answer: there is no picture attached or equation? what's the question?

Step-by-step explanation:

ok, what do you need help with?

Answer:

y-intercept = 3

Step-by-step explanation:

value that's on the y - axis

Answer:

10t + D = 40

Step-by-step explanation:

y = mx + b is the equation of a line in slope intercept form. We'll be using this equation since the slope, or distance traveled, is steady (linear). In this case, the slope is 10 since Sarah's pace is 10 km/hr. m is the slope, so m = 10.

y = 10x + b. However, she needs to run 40 km. So we're going to substitute 40 in for y.

40 = 10x + b. Now, we need to use t instead of x since that's what's been asked of us. (The slope represents the distance traveled over time, so t fits.)

10t + b = 40

b needs to become D, the distance in kilometers.

So now we have 10t + D = 40

Answer:

D(t)= 40-10t

Step-by-step explanation:

#KmNn

Answer:

17.00 and 17,000.00

this is your answer to ur question

The shape is an irregular pentagon

Answer:

7

Step-by-step explanation:

[tex]s = {a}^{2} \: thus \: a = \sqrt{s } = \sqrt{49} = 7[/tex]

Answer:

1 ) 0.023

2 ) 0.1004

Step-by-step explanation:

2 / 100 + 3 / 1000

= 0.02 + 0.003

= 0.020 + 0.003

= 0.023

1 / 10 + 4 / 10,000

= 0.1 + 0.0004

= 0.1000 + 0.0004

= 0.1004

Answer:

2x

Step-by-step explanation:

Just solve the function operation:

f/g=(2x/2x+1)/(1/2x+1) = 2x since (2x/1)/(2x+1/2x+1) simplifies to 2x/1 the answer is 2x

Answer:

36 degrees

Step-by-step explanation:

First, to find the exterior angle of a polygon, we must divide 360 by the number of sides/angles that the specific polygon has. In this case, our polygon has 10 sides, so it's a decagon.

If we apply this formula, where s = # of sides, we can find the exterior angle of this polygon:

360/s = exterior angle

360/10 = 36

Therefore, the exterior angle is 36 degrees.

Answer:

36°

Step-by-step explanation:

Sum of exterior angles of a polygon = 360°

Part (i)

We have 60 students total, and 5 didn't like any of the two subjects, so that must mean 60-5 = 55 students liked at least one subject.

=========================================================

Part (ii)

We have 15 who like math only, 20 who like science only, and 55 who like either (or both). Let x be the number of people who like both classes.

We can then say

15+20+x = 55

x+35 = 55

x = 55-35

x = 20

This means 20 people liked both subjects

=========================================================

Part (iii)

There are 15 people who like math only, and 20 who like both. Therefore, there are 15+20 = 35 people who like math (and some of these people also like science)

=========================================================

Part (iv)

We'll follow the same idea as the previous part. There are 20 people who like science only and 20 who like both subjects. That yields 40 people total who like science (and some of these people also like math).

=========================================================

Part (v)

We'll draw a rectangle to represent the entire group of 60 students. This is considered the universal set. Inside the rectangle will be two overlapping circles to represent math (M) and science (S).

We'll have 15 go in circle M, but outside circle S to represent the 15 people who like math only. Then we have 20 go in circle S but outside circle M to show the 20 people who like science only. We have another copy of 20 go in the overlapped region between the circles. This is the 20 people who like both classes. And finally, we have 5 go outside both circles, but inside the rectangle. These are the 5 people who don't like either subject.

Note how all of the values in the diagram add up to 60

15+20+20+5 = 60

This helps confirm we have the correct values.

Look in the images it is solved.

Answer:

Cost of 1 goggles = $20

Cost of 1 mask = 15

Step-by-step explanation:

Given:

Cost of 2 goggles and 1 mask = $55

Cost of 1 goggles and 2 mask = $50

Find:

Cost of each goggles and mask

Computation:

Assume;

Cost of 1 goggles = a

Cost of 1 mask = b

So,

2a + b = 55.....EQ1

a + 2b = 50.......EQ2

EQ1 x 2

4a + 2b = 110 ......EQ3

EQ3 - EQ2

3a = 60

a = 20

Cost of 1 goggles = $20

a + 2a = 50

20 + 2b = 50

2b = 30

b = 15

Cost of 1 mask = 15

.

Answer:

The answer is "[tex]f(x) = 3(1.05)x + 2[/tex]".

Step-by-step explanation:

She starts off with 3 hours with pop music.

Next month, she will have 3 hours she has had and + 3*0.05.

3hrs + 3*0.05hrs = 3*1.05 hrs

We add 2 hours of classical music to the 3 * 1.05 hours to achieve 3 * (1.05) hours + 2 hours of classical music.

Answer: f(x):2(0.05)^x+3

Answer:

0.04

Step-by-step explanation:

2 / 50 is the same as 1 / 25.

1 / 25 = 0.04

Answer:

0.04

Step-by-step explanation:

Answer:

[tex]m<NLM = 30[/tex]

Step-by-step explanation:

1. Approach

The easiest way to solve this problem is to find the degree measure of the parameter (x). Use the fact that line (LN) is a diameter to solve for (x), beacause the angle measure of a circle on either side of the diameter is (180) degrees. One can then find the measure of arc (mNM), and then find the measure of the angle (<NLM) using the inscribed angles theory.

2. Find the measure of (x)

A diameter is the largest chord or segment in a circle. It intersects a circle at two points and runs through the center of a circle. The degree measure of a circle on either side of the diameter is (180) degrees. As per the given image, line (LN) is a diameter. The arcs (mLM) and (mNM) make up half of the circle, or rather one side of the diameter. With this information, one can form an equation and solve for the parameter (x) using this information:

[tex](mLM)+(mNM)=180[/tex]

Substitute,

[tex](mLM)+(mNM)=180[/tex]

[tex](13x-10)+(7x-10)=180[/tex]

Simplify,

[tex](13x-10)+(7x-10)=180[/tex]

[tex]20x-20=180[/tex]

Inverse operations,

[tex]20x-20=180[/tex]

[tex]20x=200[/tex]

[tex]x=10[/tex]

3. Find the measure of angle (<NLM)

The inscribed angles theorem states that an angle with its vertex on the circumference (outer edge) of a circle is equal to half of the surrounding arc. One can form an equation and solve for the measure of angle (<NLM).

[tex]m<NLM=\frac{1}{2}(mNM)[/tex]

Substitute,

[tex]m<NLM=\frac{1}{2}(mNM)[/tex]

[tex]=\frac{1}{2}(7x-10)[/tex]

[tex]=\frac{1}{2}(7(10)-10)\\\\=\frac{1}{2}(70-10)\\\\=\frac{1}{2}(60)\\\\=30[/tex]