Simplify.

14+4(12−34)2

Answer:

The distance between the two points is [tex]\sqrt{85}[/tex] units

Step-by-step explanation:

Let us revise the rule of the distance between two point [tex](x_{1},y_{1})[/tex] and  [tex](x_{2},y_{2})[/tex]

[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]

∵ We need to find the distance between the two points (8, -7) and (1, -1)

→ Let [tex]x_{1}[/tex] = 8 and [tex]x_{2}[/tex] = 1

→ Let [tex]y_{1}[/tex] = -7 and [tex]y_{2}[/tex] = -1

→ Substitute their values in the rule above

∴ [tex]d=\sqrt{(1-8)^{2}+(-1--7)^{2}}[/tex]

∴ [tex]d=\sqrt{(-7)^{2}+(-1+7)^{2}}[/tex]

∴ [tex]d=\sqrt{49+36}[/tex]

∴ [tex]d=\sqrt{85}[/tex]

→ Simplify the radical

∵ 85 = 5 × 17

→ Both of them are prime numbers

∴ The simplest form of [tex]\sqrt{85}[/tex] is [tex]\sqrt{85}[/tex]

∴ The distance between the two points is [tex]\sqrt{85}[/tex] units

Answer:

a. –4(5x) = 12; OPEN

b. 4 x 6 = 24; TRUE

c. a + 4 = 6, when a = 2; TRUE

d. 4x = 19, when x equals 5; FALSE

Step-by-step explanation:

a. –4(5x) = 12 [-20x = 12 {Divide -20 from both sides} x = -0.6 So, if x is = -0.6, then it is true, so OPEN.

b. 4 x 6 = 24 [4 x 6 = 24 so TRUE]

c. a + 4 = 6, when a = 2. (Plug 2 in for a) 2 + 4 = 6; 6 = 6; TRUE

d. 4x = 19, when x equals 5. (Plug 5 in for x) 4(5) = 19; 20 is not = 19; FALSE

Answer:

Total distance = 5.754 km

Step-by-step explanation:

Red lines of the right triangle show the layout of the race course.

Total length of the race course = Perimeter of the triangle

Perimeter of the triangle = Sum of the measures of all three sides

                                         = 1.83 + 1.524 + 2.4

                                         = 5.754 km

Therefore, total distance of the race course is 5.754 km.

Answer:

5.754

Step-by-step explanation:

Answer:

The area of the triangle DEF is 10.

Step-by-step explanation:

Area of a Triangle:

A triangle of base B and height H (both must be perpendicular) has an area of:

[tex]\displaystyle A=\frac{BH}{2}[/tex]

The image below shows the triangle formed by the points DEF. It's important to notice the points E and F lie on the same horizontal line because they both have the same y-coordinate.

This fact simplifies the calculations since we can easily compute the length the of base as the difference of their x-coordinates:

B=3-(-2)=3+2=5

Being the base of a horizontal line, the height of the triangle can be calculated as the difference of y-coordinates of D and the height of that line.

H=2-(-2)=4

With these two values, we calculate the area:

[tex]\displaystyle A=\frac{5*4}{2}=10[/tex]

The area of the triangle DEF is 10.

Answer:

True

Step-by-step explanation:

this is because when reduced to their most simple terms they are the same so:

4:8 divide both sides by 4 and get:  1:2

32:64 divide both sides by 32 and get:  1:2 as well

Answer:

Jim is correct.

Step-by-step explanation:

Given that:

Total people = 100

People who exercise in morning = 35

People who exercise in the afternoon= 45

People who exercise in the evening = 20

Ratio claimed by Tara = 33:55, 48:88, and 20:65

Ratio claimed by Jim = 35:100, 45:100, and 20:100

To find:

who is correct ?

Solution:

Looking at the ratio claimed by Tara, the ratio are number which are not known to us.

Therefore, the ratio claimed by Tara can not be correct.

Now, looking at the ratio claimed by Jim:

35:100, 45:100, and 20:100

35 is the number of people who exercise in morning.

45 is the number of people who exercise in evening.

20 is the number of people who exercise in night.

and 100 is the total number of people.

Therefore, this ratio represents the "Part-to-whole" ratio.

So, Jim is correct.

Answer:a and e for usaprebtest

Step-by-step explanation:

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Let absolute variation in the wait time at the bus stop = v

Variation = ±3 minutes

Average bus run through the city = 15 minutes

Hence, the minimum and maximum run values due to the variation can be modeled as:

|variation - average run| = ±3

|v - 15| = ±3

minimum : v = - 3 +. 15 = 12 minutes

Maximum : v = 3 + 15 = 18 minutes

Answer:

Step-by-step explanation:

│x - 3│= 15

This is the answer hope this help

It’s either b or c

It either of those.

Answer:

3

Step-by-step explanation:

The sides are congruent so you can write the equation (4x+9)=21.

Now you subtract 9 from 21 and you get 4x=12.

All you gotta do now is divide and you get x=3.

Hope this helps!:)

Answer:

132+180+ 168=480

Step-by-step explanation:

3/8 of 480= 180 (tuna)

35% of 480=168 (beef)

ratio is 132 (ham)

and adds up to 480

Answer:

Slope:-1/4 y-int: 3

Step-by-step explanation:

You can you the formula y1-y2/x1-x1 or you can look at it and find out if that makes sense

Answer:

Step-by-step explanation:

I need help

Answer:  (10) 3.2   (11) option 2   (12) option 4  

               (13) Distributive  (14) Associative

Step-by-step explanation:

10) "Absolute value" makes the number positive.

       - |-4| + |-7.2|

   =  -  4  +  7.2

   =       3.2

11) "Opposite" changes the sign.

    the opposite of   [tex]-\sqrt{\dfrac{2}{5}}[/tex]     is     [tex]+\sqrt{\dfrac{2}{5}}[/tex]

12) Reciprocal means "flip" the fraction

     the reciprocal of    [tex]-\sqrt{\dfrac{2}{5}}[/tex]     is    [tex]-\sqrt{\dfrac{5}{2}}[/tex]

13) a(b + c) = ab + ac    is the Distributive Property

     [tex]-\sqrt5(2+X)[/tex]

 =  [tex]-\sqrt5(2) -\sqrt5(X)[/tex]

 =  [tex]-2\sqrt5 -X\sqrt5[/tex]

14) a · (b · c) = (a · b) · c     is the Associative Property

    [tex]20(4\sqrt5)[/tex]

  = [tex](20\cdot 4)\sqrt5[/tex]

Complete Question

You are measuring walnuts for banana-walnut oatmeal and a spinach and walnut salad. You need 3/4 cup of walnuts for the oatmeal and 7/8 cup of walnuts for the salad. You have a 1/8 -cup scoop. Complete the descriptions of two different ways to find how many scoops of walnuts you will need. Enter all non-whole number answers as mixed numbers in simplest form.

Answer:

13 scoops

Step-by-step explanation:

Description 1

Step 1

3/4 cup of walnuts for the oatmeal

7/8 cup of walnuts for the salad

Total cups of walnuts needed for both salad and oatmeal =

3/4 cups + 7/8 cups

(3/4 + 7/8)

(6 + 7/8)

= 13/8 cups of walnuts

= 1 5/8 cups of walnuts

Step 2

You have a 1/8 -cup scoop

The number of cup scoops of walnuts need is calculated as

1 5/8 cups ÷ 1/8 cup scoop

= 13/8 ÷ 1/8

= 13/8 × 8/1

= 13 scoops

Therefore, 13 scoops of walnuts is needed.

Description 2

3/4 cup of walnuts for the oatmeal

7/8 cup of walnuts for the salad

1/8 cup scoop

Therefore,

(3/4 + 7/8) ÷ 1/8

=(13/8) ÷ 1/8

= 13 scoops of walnuts are needed

Answer:

4398046511104

Step-by-step explanation:

you multiply the exponents which results in 21 and then you do 4^21 which gets 4398046511104

Answer:

- 6

Step-by-step explanation:

Step 1:

- ( 5z + 12 ) = 18     Equation

Step 2:

- 5z - 12 = 18      Open Parenthises

Step 3:

- 5z = 30     Add 12 on both sides

Step 4:

z = 30 ÷ - 5     Divide

Answer:

z = - 6

Hope This Helps :)

Answer: z = -6

Step-by-step explanation:

Hi there! I will be showing you how to solve the given equation. If you have any questions feel free to comment it down below.

Step 1: Remove parentheses.

-5z - 12 = 18

Step 2: Add 12 to both sides.

-5z = 18 + 12

Step 3: Simplify 18 + 12 to 30.

-5z = 30

Step 4: Divide both sides by -5.

z = [tex]-\frac{30}{5}[/tex]

Step 5: Simplify [tex]\frac{30}{5}[/tex] to 6.

z = -6

I hope I helped you :)

Answer:

<MLI and <KLI

They share the same line and it's 180°

Answer:15

Step-by-step explanation: 1st multiple what’s in the parenthesis (3*3= 9 & 4*4= 16

Next write it out 22+(9-16)

Then you subtract 9 from 16 since it’s in parenthesis So it’s 22+(-7) and since you are adding a negative and a positive together you will have to subtract and keep the sign of the larger number so the answer is 15 since u needed to subtract but 22 is the larger number making it positive answer

Answer:

x = -5

Step-by-step explanation:

Since these two triangles are similar, the ratio between the corresponding lengths of each triangle will be the same.

This means the ratio between one side of each triangle (e.g. AD and DC) will be the same as the ratio between a different side of each triangle (e.g. BE and BC).

So, to create an equation for the sides which contain the unknown 'x', we must first find the ratio between the two sides by using a different set of sides.

On the right side we are given 9 for AD, and 18 for DC.

9/18 = 0.5

This means that the extra length of the larger triangle from the smaller one (AD) is half the length of the smaller triangle (DC). We can use this to make an equation for x:

If AD/DC = 0.5, then BE/EC will also = 0.5

BE = x+23

EC = x+41

Therefore:

[tex]\frac{x+23}{x+41} = 0.5[/tex]

Now we can solve by multiplying both sides by x+41 to eliminate the fraction:

[tex]x+23=0.5(x+41)[/tex]

Now we multiply out the brackets and move the terms to different sides:

[tex]x+23=0.5x+20.5[/tex]

[tex]0.5x = -2.5[/tex]

[tex]x = -5[/tex]

And if we substitute the -5 into the equations:

-5+23 = 18

-5 + 41 = 36

We will see that -5 does indeed give us the same ratio between the lengths:

18/36 = 0.5

Hope this helped!

Answer:

x = 57.59

Step-by-step explanation:

979 * 1 / 17

x = 57.59

cross multiply then divide.

if you want to be thorough and make the equation

17x = 979(1)

x = 57.59  

Answer: Add, subtract, multiply, divide

Step-by-step explanation:

Terms must be like terms in order to add or subtract. Terms do not have to be like if we are multiplying or dividing.

You cant add unlike terms when adding or subtracting, but you can use the exponent rules when multiply or dividing.

Answer:

y=0

Step-by-step explanation:

Answer:

Step-by-step explanation:

y=0

Answer:

A

Step-by-step explanation:

did it on edge

Answer:

A. 4(cos(x)-cos^2(x))

Step-by-step explanation:

Did the quiz on edge

Answer: 490.63

Step-by-step explanation: