Use the drawing tools to form the correct answer on the provided graph. Graph the following step function.
f(x)=-2; x <-3
1; -3 3; x>2

Let’s solve the equation x^2 - 4x = 5 by factoring:

First, we’ll move all the terms to one side of the equation:

x^2 - 4x - 5 = 0

Now, we’ll factor the left side of the equation. We’re looking for two numbers that multiply to -5 and add to -4. Those numbers are -5 and 1. So we can write:

(x - 5) (x + 1) = 0

Now we’ll use the zero-product property to solve for x. This property states that if the product of two numbers is zero, then at least one of the numbers must be zero. So we have:

x - 5 = 0 or x + 1 = 0

Solving each equation separately, we find that x = 5 or x = -1.

So, the solutions to the equation x^2 - 4x = 5 are x = 5 and x = -1.

Answer:

x = 1.5 +/-√3.25.

Step-by-step explanation:

x^2 - 3x - 1 = 0

x^2 - 3x = 1

Completing the square:

(x - 1.5)^2 - 1.5^2 = 1

(x - 1.5)^2 = 1 + 2.25 = 3.25

x - 1.5 = +/-√3.25

x = 1.5 +/-√3.25

Answer: 6

Step-by-step explanation:

Lets re- write the numbers in growing order.

2,3,4,6,7,10,10

The number that stays exactly in the middle of the the sequence is the median.

Number 6 stays in the middle. So 6 is the median

Answer

Step by step explanation

Given data : 4 , 3 , 2 , 10 , 10 , 6 , 7

Arranging the data in ascending order, we have,

2 , 3 , 4 , 6 , 7 , 10 , 10

Here, n ( total number of items) = 7

Now, position of median:

\( {( \frac{n + 1}{2}) }^{th} \) item

plug the value

\( = {( \frac{7 + 1}{2} )}^{th} \) item

Add the numbers

\( =( { \frac{8}{2} )}^{th} \) item

Divide

\( = {4}^{th} \) item

i.e 4th item is the median

Median = 6

------------------------------------------------------------------------

Further more explanation:

Let's take another example:

please see the attached picture.

In the above series, the numbers are arranged in ascending order. Here, the fourth item 17 has three items before it and three items after it. So, 17 is the middle item in the series. 17 is called the median of the series.

Thus, Median is the value of the middle - most observation, when the data are arranged in ascending or descending order of magnitude.

Hope I helped..

Best regards!!

Answer: x = - 6

y = 7

Step-by-step explanation:

Let 2x -5y = -47 be eq. 1

And 6x -5y = -71 be eq. 2

By substrate of 1 - 2:

2x-5y-6x+5y = -47+71

so -4x=24 and x= -6

Substitute x in any eq.

2(-6) - 5y = -47

-5y = -47 +12

-5y = -35 so y= 7

9514 1404 393

Answer:

  x = 5

Step-by-step explanation:

The two triangles are similar by the ASA theorem. The ratio of long side to short side in each right triangle is the same:

  x/3 = 7.5/4.5

  x = 3(7.5/4.5) . . . . multiply by 3

  x = 5

Answer:

52

Step-by-step explanation:

RTQ is 52 because if PTR is a right angle, right angles equal 90 degrees. So if PTQ is 38 degrees, we subtract 38 from 90 to get RTQ. 90-38 equals 52.

Answer:

52 degrees

Step-by-step explanation:

right angle = 90

90-38=52

So RTQ = 52 degrees

The first missing number in the sequence is 35, and the last missing number is 77.

The two missing numbers in the given sequence is calculated as follows;

= ?    49     63    ?

The given sequence is factor 7 which increases by 2

= 7 x 5      7 x 7       7 x 9     7 x 11

= 35         49          63          77

Thus, the first missing number in the sequence is 35, and the last missing number is 77.

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The sequence's initial missing number is 35, and its last missing number is 77.

The following number in the list is

The two missing numbers are determined as follows for the given sequence:

= ? 49 63 ?

The sequence is factor 7, which rises by 2 in the specified order.

= 7 x 5      7 x 7       7 x 9     7 x 11

= 35         49          63          77

Thus, the first missing number in the sequence is 35, and the last missing number is 77.

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Answer:

OK, Here is your answer

Step-by-step explanation:

Let's assume the capacity of the drum be C litres.Since the drum is initially 3/4 full, the amount of water in it is 3/4 × C = (3/4)C liters.When 9 liters of water are drawn from the drum, the remaining amount of water is (3/4)C - 9 liters.Since the drum is now half full, the amount of water remaining in it is (1/2)C liters.Therefore, we can write the equation: (3/4)C - 9 = (1/2)CTo solve for C, let's first get rid of the fractions by multiplying both sides by 4.(3/4)C - 9 = (1/2)C → 3C - 36 = 2C → C = 36Therefore, the capacity of the drum is 36 liters.Hence, the drum holds 3/4 × 36 = 27 liters of water initially and after 9 liters of water are drawn, the remaining amount of water in it is 27 - 9 = 18 liters.

Answer:

18 Lieters.

Step-by-step explanation:

found the answer in his answer. ↑↑↑↑

Answer:

The mean absolute deviation is 2. Hope this helps

Step-by-step explanation:

7+2+8+9+9+5+6+8+1=5.5

7-5.5=1.5

5.5-2=3.5

8-5.5=2.5

9-5.5=3.5

9-5.5=3.5

5.5-5=0.5

6-5.5=1.5

8-5.5 2.5

5.5-1=4.5

1.5+3.5+2.5+3.5+3.5+0.5+1.5+2.5+4.5=2

Answer is 2.

I hope this can help!

Have a nice day :)

~Amy

the left side of this equation equal the right side through the process of completing the square that establishes the equality between the left side and the right side of the Gaussian integral equation.

using  completing the square method:

Starting with the left side of the equation:

∫\(e^(^-^x^2)\) dx

\(e^(^-^x^2) = (e^(^-x^2/2))^2\)

∫\((e^(^-^x^2/2))^2 dx\)

let  u = √(x²/2) =  x = √(2u²).

dx = √2u du.

∫ \((e^(^x^2/2))^2 dx\)

= ∫ \((e^(^-2u^2)\)) (√2u du)

The integral of \(e^(-2u^2)\)= √(π/2).

∫ \((e^(-x^2/2))^2\) dx

= ∫  (√2u du) \((e^(-2u^2))\\\)

= √(π/2) ∫ (√2u du)

We substitute back  u = √(x²/2), we obtain:

∫ \((e^(-x^2/2))^2\)dx

= √(π/2) (√(x²/2))²

= √(π/2) (x²/2)

= (√π/2) x²

A comparison  with the right side of the equation  shows that they are are equal.

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Answer:

C! Simply solve for X.

Remove the parenthesis,

Move the terms,

Combine the like terms,

Divide both sides.

Answer:

16/75, D

Step-by-step explanation:

6/5*1/3. We can cross simplify to make it 2/5*1/1. That is 2/5. Then, 2/5*8/15 is 16/75 which is answer choice D.

The first thing you do is find the amount of boys in the club.

since 32 is combined and 18 is the # of girls, you are going to subtract the girls from the combination of both.

32 - 18 = 14

Then, since it says girls to boys, you will put the number of girls first and the boys second.

ie: 18:14

hopefully this helps <3

After cοmpleting the task, we can state that The whοle number clοsest tο  expressiοn 7.141 is 7. Therefοre, √51 is clοsest tο the whοle number 7.

The whοle numbers are the part οf the number system which includes all the pοsitive integers frοm 0 tο infinity. These numbers exist in the number line. Hence, they are all real numbers. We can say, all the whοle numbers are real numbers, but nοt all the real numbers are whοle numbers.

Thus, we can define whοle numbers as the set οf natural numbers and 0. Integers are the set οf whοle numbers and negative οf natural numbers. Hence, integers include bοth pοsitive and negative numbers including 0. Real numbers are the set οf all these types οf numbers, i.e., natural numbers, whοle numbers, integers and fractiοns.

√51 is apprοximately equal tο 7.141. The whοle number clοsest tο 7.141 is 7.

Therefοre, √51 is clοsest tο the whοle number 7.

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9514 1404 393

Answer:

  (3, 1)

Step-by-step explanation:

The lines on the graph cross at the point (x, y) = (3, 1). That is the solution to the system of equations.

Answer:

the lcm would be 30 not 60

Step-by-step explanation:

Answer:

the least common multiple is 30 but instead she found the greatest common mutiple.

Step-by-step explanation:

The current weight of the truck is given as follows:

3496 kg.

The current weight of the truck is obtained applying the proportions in the context of the problem.

The initial weight of the truck is given as follows:

3796 kg.

The weight removed from the truck is given as follows:

6 x 50 = 300 kg.

Hence the current weight of the truck is given as follows:

3796 - 300 = 3496 kg.

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Answer:

Explained below.

Step-by-step explanation:

The (1 - α)% confidence interval for the population proportion is:

\(CI=\hat p\pm MOE\)

Given:

\(\hat p=0.40\\MOE=0.03\)

(a)

Compute the confidence interval as follows:

\(CI=\hat p\pm MOE\)

     \(=0.40\pm0.03\\\\=(0.37, 0.43)\)

(b)

Since the confidence interval consists of values less than 50%, it implies that there is not enough evidence to suggest that more than 50% of Americans approve of Trump.

Using percentage we know that the correct option is (B) Reed is happy and relieved that he will have insurance.

Alan buys tickets online:

As, $36.3 > $35.

So it does not make sense that Alan would buy a ticket online, which is an option (A).

Option (D):

Therefore, using percentage we know that the correct option is (B) Reed is happy and relieved that he will have insurance.

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The given question where we  randomly select a chocolate. It is a milk chocolate or dark chocolate is a mutually exclusive chocolate

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Statistics is the study of occurrences that follow a probability distribution. Probability is a measure of how likely something is to occur. The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event might occur.

In the given question

we see

Selecting a milk chocolate or dark chocolate is mutually exclusive event as they are not related to each other

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To write 28 + 24 as a product of two factors, we need to determine the HCF of the addends (28 and 24). This can be done by listing the factors of the addends. The greatest factor that is common in 28 and 24 is the HCF.

If the number is in bolded text, the number is a common factor.

Since 4 > 2 > 1, the HCF is 4.

Now, let us put the provided expression between parentheses.

Finally, factor four out of the expression, as it is the GCF of 28 and 24.

Therefore, 28 + 24 as a product of two factors is 4(7 + 6).

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Answer:

There are 3 mini hotdogs and 6 chicken wings in the combination meal.

Step-by-step explanation:

Variable Definitions:

​x=the number of mini hotdogs in the meal

y=the number of chicken wings in the meal

Each mini hotdog has 100 calories, so x mini hot dogs would have 100x100x calories. Each chicken wing has 50 calories, so  y chicken wings would have 50y calories. Therefore, the total number of calories 100x+50y equals 600:

100x+50y=600

Since the combination meal has twice as many chicken wings as mini hot dogs, there are more chicken wings, so if we multiply 2 by the number of mini hot dogs, we will get the number of chicken wings, meaning y equals 2x.

y=2x

Write System of Equations:

​100x+50y=600

y=2x

Solve for y in each equation:

100x+50y=600

50y=−100x+600

y=−2x+12

The x variable represents the number of mini hotdogs in the meal and the y variable represents the number of chicken wings in the meal. Since the lines intersect at the point (3,6) we can say:

There are 3 mini hotdogs and 6 chicken wings in the combination meal.

​

There are 3 mini hot dogs and 6 chicken wings in the combination meal.

​x=the number of mini hot dogs in the meal

y=the number of chicken wings in the meal

Each mini hot dog has 100 calories,

so x mini hot dogs would have 100×100x calories.

Each chicken wing has 50 calories, so  y chicken wings would have 50y calories.

Therefore, the total number of calories 100x+50y equals 600:

100x+50y=600

Since, the combination meal has twice as many chicken wings as mini hot dogs, there are more chicken wings,

so, if we multiply 2 by the number of mini hot dogs, we will get the number of chicken wings, meaning y equals 2x.

y=2x

​100x+50y=600

y=2x

Solve for y in each equation:

100x+50y=600

50y=−100x+600

y=−2x+12

The x variable represents the number of mini hot dogs in the meal, and the y variable represents the number of chicken wings in the meal.

Since the lines intersect at the point (3,6) we can say:

Therefore, there are3 mini hot dogs and 6 chicken wings in the combination meal.

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In parabola, the vertex of b(x) is 8 units to the right of the vertex of .

What is parabola in math?

A parabola is a U-shaped plane curve in which every point is situated at an equal distance from both the focus, a fixed point, and the directrix, a fixed line. All of the parabola-related ideas are discussed here since it is a crucial component of the conic section subject. When f(x)=ax² +bx +c, where a, b, and c are real integers and a0, the function is said to be quadratic.

f(x) = x²

b(x) = f(x - 8)

f(x) = x²

f(x- 8) = (x- 8)²

f(X-8) = x² - 16x + 64

b(X) =  f(x- 8) = x² - 16x + 64

Comparing  b(X)  = x² - 16x + 64 with  y = ax² + bx + c

 a = 1, b = -16 , c = 64

-b/2a =  8  ...........1

Hence, the x-coordinate of vertex is 8.

putting x = 8 in b(x)

b(8) = 8² - 16 * 8 + 64 = 0

     So, the vertex of b(x)  is (8,0)

Comparing f(x) = x²  with y = ax² +bx+c

  a = 1 , b= 0 , c = 0

  -b/2a = 0 .........2

 Hence, the x-coordinate of vertex is 0.

putting  x = 0 in f(X)

f(0) = 0² = 0

So, the vertex of  f(x) = (0,0)

Thus, the vertex of b(x) is 8 units to the right of the vertex of .

(Option A is false.)

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I think the answers 3048_&8_9_)_)_

The number of children in the group based on the information is 13.

Total number of cookies Abby baked = 124

Number of cookies remaining after children left the kitchen = 7

Number of cookies taken by the group of children = 124 - 7 = 117

Given that 117 cookies were equally shared by the children.

Let the number of children be x.

Number of children was more than 10 and less than 30

10 < x < 30

x will always be an integer.

Let a number of cookies each child took be c.

The prime factorization of 117 is 3*3*13.

As 117 = x * c

117, when written as the product of 2 numbers, that is x*c form, will be as given below:

1*117, 3*39, 9*13, 13*9, 39*3, 117*1

Given that 10 < x < 30. Therefore, we can only take 13 * 9 as the required x * c form.

x = 13 and c = 9

Number of children in the group is 13.

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Answer:

Step-by-step explanation:

9514 1404 393

Answer:

  32°, 58°

Step-by-step explanation:

The second angle is (3x-38), and their sum is ...

  x +(3x -38) = 90

  4x = 128 . . . . . . . . . add 38 and simplify

  x = 32 . . . . . first angle

  3x -38 = 3·32 -38 = 58 . . . . . . second angle

The measures of the two angles are 32° and 58°.