The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
a. Write and solve three inequalities for the previous statement using the triangle shown.
b. What values for x make sense?

There are no real solutions for the equation x² + 20 = 4.

Equation, which is defined as the quality of being equal, is frequently represented by a mathematical expression with equal values on either side or by a situation in which numerous factors must be taken into account.

Consider the equation,

x² + 20 = 4

Subtracting 20 from each side of the equation.

x² + 20 - 20 = 4 - 20

x² = - 16

√x² = √ - 16

x = ± √-16

x = ± 4√(-1)

x = ± 4i

Since i is the complex number that is equal to √-1. Therefore, there are no real solutions to the equation.

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Answer:no real number solutions

By using properties of right triangles, we will see that the value of x is 7.72

In the image we have a set of right triangles, and we want to find the value of x.

Let's look at the large triangle in the left, we know that the hypotenuse measures 18 units and one angle measures 64°, with that information we can get the adjacent side (the dashed line, let's call it A) to that angle:

Cos(64°) = A/18

18*cos(64°) = A = 7.05

Now we know one of the cathetus of the smaller right triangle (the one we can see in the right side). Here we know one angle that measures 20° and the opposite to that angle measures 7.05

Then the value of x is given by the equation:

x = 7.05/sin(20°) = 7.72

We conclude that the value of x is 7.72

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Answer:  A vertical stretch of f(x)f(x) is of the form g(x)=kf(x)g(x)=kf(x) where k>1k>1. A vertical stretch of 5 then means that g(x)=5f(x)=5(x+2)=5x+10g(x)=5f(x)=5(x+2)=5x+10.

Step-by-step explanation: so i really hope this helps <3 (:

Answer:

ones

Step-by-step explanation:

always start with the smallest number

Answer:

ones

then tens, tenths, hundreths

Step-by-step explanation:

hope this helps

Answer: 15,552 inches cubed

Hope this helps!

Answer:

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

2 times 2 equals 4, 4 times 3 gets you 12.

the exponent 2 above the original 2 simply means to just times the original number by 2.

Note:

Love your handwriting!  

The percent of change is an increase in altitude of the weather balloon.

Change in altitude = New altitude - Original altitude

= 103 ft - 100 ft

= 3 ft

Percentage change = Change in altitude / Original altitude × 100

= 3 / 100 × 100

= 3%

Therefore, the percentage change in the altitude of the weather balloon is 3%.

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The volume of the toy box is 24 cubic feet.

Remember that for a rectangular prism of length L, width W, and height H the volume is given by the formula:

V = L*W*H

In this case, we know that:

L = 4ft

W = 3ft

H = 2ft

Replacing that in the volume formula we get.

V = 4ft*3ft*2ft = 24ft^3

The volume of the toy box is 24 cubic feet.

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Answer:

4 hr

Step-by-step explanation:

Answer:

Mean = 260.45

Median = 284

Mode = 287, 285  (there are 2 modes)

Since it is a championship sports team , it is likely that this data is representative of all players in that league

Step-by-step explanation:

Mean = Sum of the weights/11 = 2865/11 = 260.45

Median is the middle of the data set when the data values are arranged in ascending order

In ascending order: 206, 216, 217, 235, 273, 284, 285, 285, 287, 287, 290

Mode is the value that occurs the maximum number of times in a data set

Here there are 2 modes 285 and 287 both of which occur twice

Answer:

2.4×10−6

Step-by-step explanation:

Answer: 63,960

Step-by-step explanation:

Answer:

$63960

Step-by-step explanation:

tbh if i made that salary tho

Step-by-step explanation:

15x²-14x+3

Product =45

Sum=-14

=(-9,-5)

15x²-9x-5x+3

3x(5x-3)-1(5x+3)

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

The correct answer is option c. $0.79

As per the question:

No. of pea cans in a case = 18 cans

Weight of each can of peas = 12 ounces

Price of a case of peas = $14.22

The information regarding the weight of each can is redundant in this question and therefore, is not used for solving the question

Therefore, the formula to be used for solving:

Price per unit can of peas= (Price of a case of peas/No of pea cans in a case)

Price per unit can of peas= ($14.22/18)

The price per unit can of peas= $0.79

Hence, option c is the correct answer

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The value of 165 pounds is 74.8 kilograms

The given parameter is:

1 kilogram = 2.205 pounds

Multiply both sides by 165

So, we have

165 * 1 kilogram = 2.205 pounds * 165

Divide both sides by 2.205

So, we have

165/2.205 * 1 kilogram = 2.205 pounds * 165/2.205

Evaluate the products

So, we have

74.8 kilogram = 165 pounds

Rewrite as

165 pounds = 74.8 kilogram

Hence, the value of 165 pounds is 74.8 kilograms

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The probability that a randomly chosen participant in the survey will have visited both England and France is 0.5

Given data

number of clients = 70

travelled to England , France or both = 60

travelled to England = 45

travelled to France = 50

let:

E represent the client that visited England only,

F represent the number of client that visited France only,

EF represent the number of clients that visited both England and France only

we have

E + F + EF = 60

45 - EF + 50  - EF + EF = 60

45 + 50 - EF = 60

95 - EF = 60

95 - 60 = EF

EF = 35

E = 10

F = 15

probability

Pr = required outcome / possible outcome

= EF / clients surveyed

= 35 / 70

= 0.5

Explanation

EF represents the number of clients that visited England and France only, and it was solved to be 35. probability is the ratio of required outcome which 35 to the possible outcome which is the total number of clients 70. The ratio gives 0.5

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oopss wrong one my bad

Answer:

2

Step-by-step explanation:

18x -12 = 18x -12 +2

18x -12 = 18x -10

18x cancel each other out

-12 = -10

-12 + 12 = -10 + 12

add 12 to each side

= 2

Answer:

  x = 12

Step-by-step explanation:

Given congruent triangles ABD and CBD, and expressions for corresponding angles ABD and CBD, you want the value of x in the expression for angle CBD.

Corresponding parts of congruent triangles are congruent, so we know ...

  ∠ABD ≅ ∠CBD

  99° = (9x -9)° . . . . use the given expressions

  11 = x -1 . . . . . . . . divide by 9°

  12 = x . . . . . . . . add 1

The value of x is 12.

Answer:

Step-by-step explanation:

A

Answer: Nachelle is 1.35 meters tall. At 2 p.m., she measures the length of a tree's shadow to be 24.15 meters. She stands 19.2 meters away from the tree, so … that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.

Step-by-step explanation:

Answer:

The question isn't clear but i try to do for 7-(-1) solution only. 7-(-1) =8 mean that 7+1=8

According to the given statement One and half hour after the summer thunderstorm began, the temperature was approximately 1.0°F flower than at the start of the storm.

Subtract the final temperature from the starting temperature to get the temperature change (T). Multiply the temperature change by the sample's mass. Share the product's energy and heat output.

The equation is C = Q / (T m).

Consider the function t as defined below. t(h)=9.5h – 15.52 +17.4h-10.12

Here,

h is the number of hours after storm began.

The function t represents the rate of change of temperature in °F per hour during the hour and a half after the storm began.

During the storm, the temperatures lowers and then rises.

One and half hour after the summer thunderstorm began, the temperature was approximately 1.0°F flower than at the start of the storm.

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Answer:

The first one I think xx

The closure property is defined as the completion of a collection of numbers by using arithmetic operations.

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variables having the highest correlation are -

A strong correlation, also known as a high correlation, indicates that two or more variables have a significant link with one another, whereas a weak or low correlation indicates that the variables are rarely associated. The process of examining the strength of such association with the use of available statistical data is known as correlation analysis.

Out of the four measures in the survey, which two variables have the highest correlation?

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Answer:

-729

Step-by-step explanation:

-9 × (-9) × (-9) =

= 81 × (-9)

= -729

The area of the shaded region in the first quadrant is: 0.75 units

The area under a curve between two points can be found by doing a definite integral between the two points.

Now,

Given:

To find: area bounded by the given lines and curve in the first quadrant.

Finding:

Now, according to the question, the lines x = 0 and y = 2 intersect at the point (0,2).

Point of Intersection of y = 2 and y = 3x - x²:

2 = 3x - x²

=> x² - 3x + 2 = 0

=> (x - 2)(x - 1) = 0

That is, the line and the curve intersect at two points: ( 1 , 2) and (2,2). But the point that is of our importance is only (1,2).

Thus, area shaded = [tex]\int\limits^1_0 {2 - 3x +x^{2}} \, dx[/tex] = 0.75 square units.

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(COMPLETE QUESTION:

What is the area in the first quadrant bounded by y=3x-x³ and the lines x=0, y=2?)