A bolt is to be made 2.0 cm long with a tolerance of 4%. Set up an equation to solve for the shortest and longest bolt length. Show your original equation and the process used to find the shortest and longest bolt length.

Answer:

y = 4x + 26

Step-by-step explanation:

There are lots of different methods to do these types of questions, but this is the way i like to do it.

Coordinate (x1, y1) : (-5, 6) and Gradient (m): 4

Start with this generic equation:

y- y1 = m(x-x1)

Substitute in the values they have given you:

y - 6 = 4(x-(-5))

This becomes:

y - 6 = 4 (x+5)

y - 6 = 4x + 20

Keep solving by moving the 6 over to the other side:

y = 4x + 20 + 6

y = 4x + 26

An easy way to double check:

1) the coefficient of x is the slope. We got 4x, and the slope is 4, so that's correct.

2) Substitute x=-5 into the equation, and we get 6, which is the exact coordinate that they gave us. This is also right.

Hope this helped : )

Answer:

Domain : [-4,4} or  [tex]-4\leq x\leq 4[/tex]

Zeros of the function: (-2, 0, 2)

Intervals when function is positive: (0,2)

Intervals where function is negative: (-4,0), (2,4)

Step-by-step explanation:

Domain can be defined as the input of all possible values of x in the given interval. We can se from the graph that minimum value of x is -4 while maximum value of x is 4. So

[tex]-4\leq x\leq 4[/tex]

The value of function becomes 0 at three places, when x becomes -2,0 or 2

We can see that the function is negative throughout the interval (-4,0), then it become positive from (0,2), then it becomes negative again from (2,4)

Answer:

$1000.73

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

first you do 11 divided by 5

then you multiply it by 2

which gives you 4.4

the closest number is 5

correct me if i am wrong

Answer:

H. 22

Step-by-step explanation:

- The car travels 11 inches every 5 seconds, so in one second it travels:

11 inches / 5 seconds = 2.2 inches/second

- In 2 minutes (120 seconds), the car travels:

2.2 inches/second * 120 seconds = 264 inches

- To convert inches to feet, we can divide by the number of inches in a foot:

264 inches / 12 inches/foot = 22 feet

Answer:

1. 10218

2. 9720

Step-by-step explanation:

1 ---------------

need to find the least 5 -digit number leaving same remainder when divided by 12, 18, 21, 28

Least 5-digit number is 10000, when it is divided by 262, we get

10000/262= 38.17

39*262= 10218, this number leaves 0 remainder when divided by all 4 given numbers, any number leaving more remainder will be greater than this

Answer: 10218

2 -----------------

Greatest 4-digit number exactly divisible by 12, 18, 40, 45

Greatest 4 digit number is 9999

9999/360= 27.78

360*27= 9720 is the greatest number we are looking for

Answer: 9720

Answer:

VX = 4n +7

explanation:

the equation is VX = n + 7 + 3n, all you need to do is add the n variables and get VX = 4n + 7.

Answer:

21

Step-by-step explanation:

n+7=3n ⇒ 2n=7 ⇒ n= 3.5

VX= 2*(n+7) = 2*(3.5+7)= 21

in case you need

WY= 2*(4n+1)= 2*(4*3.5+1)= 30

Answer:

60

Step-by-step explanation:

2x+5+x-5=180

add the common things

3x=180

divide stuff

x=60

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Hey!!

Solution,

2x+5+x-5=180( sum of co-interior angles)

or,2x+x-5+5=180

or,3x=180

or,X=180/3

X=60

The value of X is 60

hope it helps

Good luck on your assignment

Stay safe..

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Answer:

4.12

Step-by-step explanation:

[tex]\sqrt{17} = 4.1231[/tex] ≈ 4.12

Answer:

19 1/2 inches.

Step-by-step explanation:

edge 2020 OwO

Answer:

19.5 inches a.k.a. 1 foot and 7.5 inches

Step-by-step explanation:

1) To make it easier, convert Sean's dad's height into solely inches.

6 feet and 6 inches = 6(12) + 6 = 72 + 6 = 78 inches

2) Find out what is one-fourth of Sean's dad's height.

In order to do that, you must simply multiply 78 by [tex]\frac{1}{4}[/tex].

[tex]78(\frac{1}{4} ) = 19.5[/tex]

3) Convert back to feet and inches (if necessary)...

19.5 inches = 12 + 7.5 = 1 foot and 7.5 inches

I hope this helps!

Answer:

true

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

closed circles can mean greater than or equal to/less than or equal to

Answer:

Step-by-step explanation:

f(-2)=g(-2) is correct.

at x=-2,f(x)=4,g(x)=4

so f(-2)=g(-2)

Answer:

6/12

Step-by-step explanation:

[tex]\sqrt{\frac{6}{8}} × \sqrt{\frac{6}{18}}[/tex]

= 6/2√2 × 3√2

= 6/12

Answer:

B.

Step-by-step explanation:

Just find which side C is opposite to.

In this case, it is opposite to AB

Answer:

Slope = 1/5 y intercept=-8

Step-by-step explanation:

We can use sloper intercept form to find the answer

Answer:

Step-by-step explanation:

 Slope = 0.400/2.000 = 0.200

 x-intercept = 40/1 = 40.00000

 y-intercept = -40/5 = -8

Answer:

first blank ×

second blank- nothing

Step-by-step explanation:

2×46=92

Answer:

Step-by-step explanation

The person drove 128 miles in one hour

I divided 640/5 and got 128 as my answer

Answer:

For every one hour you drive 128 miles.

Step-by-step explanation:

First you would need to find the unit rate.

Divide 640 by 5

[tex]640/5=128[/tex]

Unit rate=

[tex]y=128x[/tex]

Hope this helps

Answer:

length = width + 10

4*width + 20 ≤ 90

width ≤ 17.5 feet

Step-by-step explanation:

The perimeter of a rectangle is given by:

Perimeter = 2*length + 2*width

The length needs to be 10 feet longer than the width, so we have:

length = width + 10

Using this length in the perimeter equation, we have:

Perimeter = 2*(width + 10) + 2*width = 4*width + 20

The perimeter needs to be up to 90 feet, so we have:

P ≤ 90

4*width + 20 ≤ 90

4*width ≤ 70

width ≤ 17.5 feet

the maximum width of the garden is 17.5 feet

Answer:

Once

Step-by-step explanation:

I put it into slope intercept first

(5/6)x - (2/3) = y

(2/3)x - (7/3) = y

Both lines are linear so they are straight. Since the two are not parallel or have the same slope then they will cross once.

Answer:

2 UNITS

Step-by-step explanation:

Answer:

D 1,400

Step-by-step explanation:

Species A doubles every 2 days and species B doubles every 5 days, so in 10 days, species A will double 10/2 = 5 times and species B will double 10/5=2 times. After 10 days from an initial population of 50 in each species, species A will have 50 x 2 ^5= 50 x 32 = 1,600 population while species B will have 50 x 2 ^2 = 200 population. Their difference is 1,600-200 = 1,400.

Answer:

10 inches

Step-by-step explanation:

The length of the playground in its actual size is 120 feet.

The scale drawing uses a scale of 1 inch to 12 feet.

This means that 1 inch in the drawing equals 12 feet in actual size.

Therefore, the length of the playground on the scale drawing is:

1 inch = 12 feet

x = 120 feet

Cross-multiply:

120 * 1 = 12 * x

=> x = 120 / 12 = 10 inches

The length of a side of the playground on  the scale drawing is 10 inches.

Answer: A

Step-by-step explanation:

6x + 12x + 90 = 180

18x + 90 = 180

        -90      -90

18x =90

x= 5

6(5) + 12(5) + 90 = 180

30 + 60 + 80 = 180

180= 180       It makes sense that it is A because there is one right angle which has a measure of 90 degrees and the other one have two measures 6x and 12x  and both of them have to also equal  90 degrees. So 90 pluse 6x plus 12x has to equal 180 because they all lie on a straight line and a straight line has an angle measure of 180 degrees.

Answer:a

Step-by-step explanation:

Answer:

Step-by-step explanation:

So that the denominator is a real number. I know that doesn't sound like a good reason, but it is the reason mostly by convention. You don't want complex i's floating all over the answer. There should be just one i.

Answer:

You have to multiply by the complex conjugate because the denominator has to be a real number. By multiplying the complex conjugate you can transform the denominator in to a real number.

Answer:

[tex]4\sqrt{5}[/tex] miles.

Step-by-step explanation:

From the given figure it is clear that the coordinates of Elm station are (-3,-6) and coordinates of Symphony station are (1,2).

Distance formula:

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Using distance formula, the distance between Elm and Symphony stations is

[tex]D=\sqrt{(1-(-3))^2+(2-(-6))^2}[/tex]

[tex]D=\sqrt{(1+3)^2+(2+6)^2}[/tex]

[tex]D=\sqrt{(4)^2+(8)^2}[/tex]

[tex]D=\sqrt{16+64}[/tex]

[tex]D=\sqrt{80}[/tex]

[tex]D=4\sqrt{5}[/tex]

Therefore, the distance between Elm and Symphony stations is [tex]4\sqrt{5}[/tex] miles.

Answer:

40/42 = 20/21

Step-by-step explanation:

Answer:

[tex]\frac{20}{21}[/tex]

Step-by-step explanation:

To divide fractions, multiply by the reciprocal. Therefore:

[tex]\frac{5}{6} / \frac{7}{8} = \frac{5}{6} * \frac{8}{7}[/tex]

Solve by multiplying the fraction with the reciprocal:

[tex]\frac{5}{6} *\frac{8}{7}= \frac{5*8}{6*7} = \frac{40}{42}[/tex]

Simplify:

[tex]\frac{40}{42} = \frac{20}{21}[/tex]. This is your answer!

the answer should be 49mm

28*7 / 4 = 49

Answer:49mm

Step-by-step explanation:

Answer:

Length: 84 ft

Width: 56 ft

Step-by-step explanation:

Let's define some variables first.

Call the length l and width w.

We know that w = 2/3l. Therefore, we can express w in terms of l with this expression.

Now, let's set up an equation. The flower garden is rectangular, and 280 feet of fencing are used to enclose the garden. This represents perimeter.

Remember the formula for perimeter of a rectangle: 2l + 2w

Let's substitute 2/3l for w:

2l + 2*2/3l = P

2l + 4/3l = 280

2 4/3l = 280

10/3l = 280

l = 84

Now, we know that the length is equal to 84 feet. We can multiply 84 feet by 2/3 to find the width.

84*2/3 = 56

Length: 84 ft

Width: 56 ft

Let's plug these values into the formula and see if they give us the correct perimeter:

2l + 2w = P

2*84 + 2*56 = P

168 + 112

= 280 feet

These are the correct dimensions!  

Hope this helps! You can reach out to me if you have further questions or concerns! :)

Answer:

The same number was not added to both sides.

Step-by-step explanation:

Given:

t - 8 = 65

in the next step it states something wrong, because it should have been this:

t - 8 = 65

add +8 left and right of the = sign.

t - 8 + 8 = 65 + 8

t + 0 = 73

t = 73

So the error made what's that

The same number was not added to both sides.

Answer:

The same number was not added to both sides

Step-by-step explanation:

t - 8 = 65

Add 8 to each side

t - 8+8 = 65+8

The  student added 8 on one side and 65 on the other

t = 73