Factor x2 – 3x – 28.


An x-method chart shows the product a c at the top of x and b at the bottom of x. Above the chart is the expression a x squared + b x + c.

Identify the values that should be written to complete the X diagram.

On the top:


On the bottom:


On the sides:

–7 and 4

Rewrite the expression using the numbers on the sides of the X diagram.

Use double grouping to factor the four terms.

x2 – 3x – 28 =

Answer:

X + e^(Y-5)/2

Step-by-step explanation:

X = 5^m

Y = 5^n

e^Y = n*e^5

n = e^(Y-5)

Check the picture below.

Answer:

8

Step-by-step explanation:

Answer: 2.25 x 10^18

Step-by-step explanation:

When dividing with exponents you subtract

56-38= 18

10 cancels out

(9 x 10^18) / 4

= 2.25 x 10^18

Answer:

a) 81

b) 16807

c) 100

d) 78125

PLEASE GIVE ME A BRAIN

Using the arithmetic operations, the total change in her monthly electric bill over 5 months is +$10.58

For the past 5 months,

The change in her July electric bill = +$18.02

The change in her August electric bill =  +$1.03

The change in her September electric bill = -$0.44

The change in her October electric bill = -$6.84

The change in her November electric bill = -$1.19

The total change in her monthly electric bill over 5 months = Sum of all changes in her electric bill over 5 months

= +18.02+1.03-0.44-6.84-1.19

= +$10.58

Hence, the total change in her monthly electric bill over 5 months is +$10.58

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Range = 15

Variance = 24.5Explanations

Standard deviation = 5.0

The formula for calculating the range is expressed as:

Range = Highest value - Lowest value

Range = 24 - 9

Range = 15

Calculate the variance

The formula for calculating the variance is expressed as:

Find the mean

Determine the variance

Determine the standard deviation

Answer:

x = 23 degrees

Step-by-step explanation:

Angle on a straight line = 180 degrees

therefore 180 - 75 = 105 degrees

105 + 52 = 157 degrees

Angle in a triangle is 180 degrees

therefore 180 - 157 = 23 degrees

Using the distance formula, Jet will take 2.2 hours to catch up with the airplane.

We will find the solution using distance formula.

distance formula is a formula that is used to find the distance between two points. These points can be in any dimension.

d=rt where

d is distance r is rate or speed and t is time

"distance airplane traveled" = "distance jet traveled"

Let x = hours "airplane" was flying

x-1 = hours "jet" was flying

.

180x = 330(x-1)

180x = 330x - 330

180x + 330 = 330x

330 = 150x

330/150 = x

2.2 hours = x

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Answer:

3 us cups

Step-by-step explanation:

multiply by 2

Solution

- We can plot the coordinates given using a graphing calculator as shown below:

- From the above, we can see that the sides are equal and the looks like a diamond

- Thus, the quadrilateral is a Rhombus

- Since all the angles are 90 degrees, it is also a square only that it was rotated.

- A square is a special type of rectangle, thus, the shape is also a rectangle

- A parallelogram as its opposite sides parallel and opposite angles equal. This is the same with our figure. Thus, it is also a parallelogram

Answer:

16/25

Step-by-step explanation:

1 3/5 = 8/5

8/5 x 2/5 = 16/25

The mean hourly snowfall is (5/3) centimeters per hour, which means that each hour there are 5/3 centimeters more of snow.

The mean hourly snowfall is given by the quotient between difference between the total snowfall at the two given times and the total time.

Here we have:

Initial snowfall = 2cm

Final snowfall = 7cm

Difference = 7cm - 2cm = 5cm

And that happens between 1 P.M. and 4 P.M., so we have 3 hours.

Then the mean hourly snowfall is:

M = 5cm/3h = (5/3) centimeters per hour.

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Answer:

-1(x - 5)x

Step-by-step explanation:

7x2 - 5x + 10x -8x2

7x2 + 5x -8x2

7x2 + 5x - 8x2

-1x2 + 5x

-1x2 + 5x

-x2 + 5x

7x2 - 5x + 10x - 8x2

-1 (x2 - 5x)

-1 (x2 - 5x)

-1(x - 5)x

-1(x - 5)x

Lauren will reach Andrea after 65 minutes of biking.

So, because Lauren is traveling at a speed that is one kilometer per minute slower than Andrea's and vice versa, Andrea's speed is 3/4 km/min and Lauren's is 1/4 km/min.

Lauren will have to bike the following kilometers in total:

Her speed being 1/4 km/min, the amount of time passed will be:

Therefore, Lauren will reach Andrea after 65 minutes of biking.

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Answer:

The first number is 10

The middle number is 11

The last number is 12

Answer:

2/15 mile per minute

Step-by-step explanation:

8 miles in 60 minutes is equivalent to 8/60 miles per minute

= 2/15 mile per minute

Answer:

Step-by-step explanation:

60/8=7.5

Answer:

[tex]\dfrac{1}{16}[/tex]

Step-by-step explanation:

Probability Distribution Table for X

Where X is the score on a fair, six-sided dice:

[tex]\begin{array}{|c|c|c|c|c|c|c|}\cline{1-7} x & 1 & 2 & 3 & 4 & 5 & 6\\\cline{1-7} \text{P}(X=x) \phantom{\dfrac11}&\frac{1}{6} & \frac{1}{6} & \frac{1}{6} & \frac{1}{6} & \frac{1}{6} & \frac{1}{6} \\\cline{1-7}\end{array}[/tex]

Probability Distribution Table for Y

Where Y is the score on an unfair, six-sided dice, and the probabilities of rolling numbers 2, 3, 4, 5 and 6 are equal, and the probability of rolling a 1 has a different value:

[tex]\begin{array}{|c|c|c|c|c|c|c|}\cline{1-7} y & 1 & 2 & 3 & 4 & 5 & 6\\\cline{1-7} \text{P}(Y=y) \phantom{\dfrac11}&1-5k&k&k&k&k&k\\\cline{1-7}\end{array}[/tex]

Note:  The probabilities of all the possible values that a discrete random variable can take add up to 1.

The outcomes of rolling one 3 and one 4 are:

Given the probability of rolling one 3 and one 4 is ¹/₂₄:

[tex]\implies \text{P}(X=3)\; \text{and} \; \text{P}(Y=4) \; \text{or} \; \; \text{P}(X=4) \; \; \text{and} \; \; \text{P}(Y=3)=\dfrac{1}{24}[/tex]

[tex]\implies \dfrac{1}{6} \times k +\dfrac{1}{6} \times k=\dfrac{1}{24}[/tex]

[tex]\implies \dfrac{k}{6} + \dfrac{k}{6}=\dfrac{1}{24}[/tex]

[tex]\implies \dfrac{2k}{6}=\dfrac{1}{24}[/tex]

[tex]\implies 24(2k)=6[/tex]

[tex]\implies 48k=6[/tex]

[tex]\implies k=\dfrac{1}{8}[/tex]

Therefore:

[tex]\implies 1-5k=1-\dfrac{5}{8}=\dfrac{3}{8}[/tex]

Hence, the probability distribution table for the unfair 6-sided dice is:

[tex]\begin{array}{|c|c|c|c|c|c|c|}\cline{1-7} y & 1 & 2 & 3 & 4 & 5 & 6\\\cline{1-7} \text{P}(Y=y) \phantom{\dfrac11}&\frac{3}{8} & \frac{1}{8} & \frac{1}{8}& \frac{1}{8} & \frac{1}{8}& \frac{1}{8} \\\cline{1-7}\end{array}[/tex]

There is only one possible outcome of rolling two 1's, so the probability of rolling two 1's is:

[tex]\implies \text{P$(X=1)$ and P$(Y=1)$}=\dfrac{1}{6}\times\dfrac{3}{8}=\dfrac{3}{48}=\dfrac{1}{16}[/tex]

Note:  Please see attachment for the sample-space diagram showing the possible outcomes of rolling two dice. The possible outcomes of rolling one 3 and one 4 are highlighted in yellow. The possible outcome of rolling two 1's is highlighted in blue.

Answer:

2°C

Step-by-step explanation:

-3 + 5 = 11

Answer:

The temperature is 3°

Step-by-step explanation:

If we start at -3, then we go to -2, then -1, then 0, then 1 and then 2.

If the function 5x+ y = 1 has the domain {-2, 1, 6}, then {11, -4, -29}  is the corresponding range  and the  answer to your question is: letter D

Function   5x + y = 1

Domain        {-2, 1, 6}

Process

Domain is the possible values of the independent variable.

Range is the values of the dependent variable.

Evaluate the function with each of the domain values to get "y"

When x = -2

 5(-2) + y = 1

  -10 + y = 1

   y = 10 + 1

     y = 11

When x = 1

 5(1) + y = 1

 5 + y = 1

 y = -5 + 1

  y = -4

When x = 6

5(6) + y = 1

30 + y =1

 y = 1 - 30

y =  -29

Range = { 11, -4 , -29}

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Answer: 9

Step-by-step explanation:

[tex]3(2y+1)[/tex] I believe is the solution you seek.

You factor 3 out of 6y + 3, leaving you with the solution.

Hope this helps!

The correct option is A: None; the mode stayed the same.

Mode of a data set is the value that occur most frequently in a data set.

There may be no mode, one mode or more than one mode for a data depending on the number of times values are repeating.

Given that before Samuel taking a test,

Mean = 84.6

Median = 82

Mode = 88

After Samuel took the test,

Mean = 84

Also given that, his score was different from every other students’ score.

This means that from the data of scores, Samuel's score is not repeating.

Mode is the most repeating element.

So Samuel's score does not effect the mode and thus stayed the same.

Hence the mode stayed the same.

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Answer: 38.8g of sugar

Step-by-step explanation:

9.7 x 4= 38.8

Answer:

x+2=3

collect like terms

x=3-2

x=1

x-12=x+30

collect like terms

x-x=30-12

=18

2(x+6)=2x+12

open bracket

2x+12=2x-12

collect like terms

2x-2x=-12+12

=0

3(x-2)=3x-2

open bracket

3x-6=3x-2

collect like terms

3x-3x=-2+6

=4

Answer:

John had 8 apples. He gave away 4. How many apples does he have left?

Step-by-step explanation: First, an arrow added 8 on the number line. Then, another arrow took away 4.  

Aaron Rodgers salary is 2.19×[tex]10^1^1[/tex] greater than his backups.

To find how many times a quantity x is greater than y we do subtraction. That is we do [tex]x-y[/tex].

So, here Aaron's salary is given to be $ 2.2× [tex]10^1^0[/tex]

And his quarterback's salary is $ 6.3×[tex]10^5[/tex].

Thus the difference between salaries= 2.2×[tex]10^1^0[/tex] - 6.3 × [tex]10^5[/tex]

                                                            = 2.19×[tex]10^1^1[/tex]

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By applying the Triangle Inequality Theorem, the number of non-identical triangles that can be made using the given side lengths is one.

In Mathematics, the Triangle Inequality Theorem can be defined as a type of theorem which states that the sum of any two (2) side lengths of a triangle must be greater than the measure of the third (2) side.

This ultimately implies that, the sum of the lengths of any two (2) sides of a triangle cannot be less than the length of the third (3) side of the triangle in accordance with the Triangle Inequality Theorem, as represented by this mathematical expression:

b - c < a < b + c

Where:

a, b, and c represent the side lengths of this triangle.

By applying the Triangle Inequality Theorem to the side lengths of this triangle, the number of non-identical triangles is given by:

5 + 7 > 10

12 > 10 (True).

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Answer:

30.

Step-by-step explanation:

Apologies if I am late, but I believe this is the answer!