what is the slope of the line through (-1, 2) and (-3, -2)

A. -1/2
B. -2
C. 2
D. 1/2

Answer: D. 10 5/6

Step-by-step explanation: K12 UNIT TEST

Alisa's house is about 99 miles from the beach

Speed is the distance travelled per unit. Mathematically, it can be expressed as:

Speed = distance / time

With above formula, we can determine the distance of Alisa's house from the beach. Details below

The following data were obtained from the question:

The distance of Alisa's house from the beach can be obtained as followed:

Speed = distance / time

Cross multiply

Distance = speed × time

Distance = 55 × 1.8

Distance = 99 miles

Thus, Alisa's house is about 99 miles from the beach

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The distance between the beach and Alisa's house is 99 miles.

Here we need to use the general relation:

Distance = Speed*Time.

Here we know that Alisa's speed is 55 miles per hour, and she drives for 1.8 hours, then we can replace:

Speed = 55 mi/h

Time = 1.8 hours

Replacing that in the distance relation we will get:

D = (55 mi/h)*(1.8 h)= 99 mi

The distance between the beach and Alisa's house is 99 miles.

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Answer:

4x(5 − x^2)

Step-by-step explanation:

20 − 4x^3

= 4x(5 − x^2)

The equivalent expression after taking a common factor is,

⇒ 2 (10 - 2x³)

What is Mathematical expression?

The combination of numbers and variables by using sign addition, subtraction, multiplication and division is called Mathematical expression.

Given that;

The expression is;

⇒ 20 - 4x³

Now, Take common factor as;

⇒ 20 - 4x³ = 2 × 10 - 2 × 2x³

                 = 2 (10 - 2x³)

Thus, The equivalent expression after taking a common factor is,

⇒ 2 (10 - 2x³)

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The drug company uses the Pre experimental design to test a new weight reduction medication.

Experimental Design:

Experimental design refers to how participants are allocated to the different groups in an experiment. Types of design include repeated measures, independent groups, and matched pairs designs.

Basically, there are 3 major types of experimental designs.

They are,

Given,

A drug company wanted to test a new weight reduction medication.

The researchers identified 500 adults from the age of 30 to 40 and randomly assigned them to two groups.

The first group received the medication and the second group received a placebo.

After 6 weeks the percentage of each group who lost more than five pounds was recorded and compared.

Here we need to find in which experimental design is used.

Here, they used the Pre-Experimental design concept,

In the Pre-Experimental concept,

They used the static group comparison method,

Basically, the process of static group comparison method is,

In a static-group comparison study, 2 or more groups are placed under observation, where only one of the groups is subjected to some treatment while the other groups are held static. All the groups are post-tested, and the observed differences between the groups are assumed to be a result of the treatment.

Therefore, in this experiment they used the Pre-Experimental design.

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Answer:

a. 2.5  

b. 2.333

c. 2.85

Step-by-step explanation:

A) 1. subtract -x on both sides              2. to get 3x-1/2=7  

3. Add 1/2 on both sides                    4. to get 3x=7.5    

5. divide 3 on both sides                   6. To get... x=2.5

B)1. Same process.                               2. x+2=13/3        

3. x=13/3-2                                         4. x= 2.33(repeating)

C) 1. same process.                           2. 2x-x/3=3+7/4

3. 2x-x/3=4.75                                  4. Isolate -x/3  

5.-x/3=4.75-2x                                    6. multiply both sides by 3          

7. -x=14.25-6x                                      8. 5x=14.25

9. x= 2.85

* remember to distribute the 3 to each variable.

Answer:

1) 4x-1/2 = x + 7

Answer : x=5/2

2) 3x + 2 = 2x+13/3

Answer: x=7/3

Step-by-step explanation:

1) 4x-1/2 = x + 7

Solution

Let's solve your equation step-by-step.

4x−1/2=x+7

Step 1: Simplify both sides of the equation.

4x+−1/2=x+7

Step 2: Subtract x from both sides.

4x+−1/2−x=x+7−x

3x+−1/2=7

Step 3: Add 1/2 to both sides.

3x+−1/2+1/2=7+1/2

3x=15/2

Step 4: Divide both sides by 3.

3x/3=15/2/3

x=5/2

2) 3x + 2 = 2x+13/3

Solution

Let's solve your equation step-by-step.

3x+2=2x+13/3

Step 1: Subtract 2x from both sides.

3x+2−2x=2x+13/3−2x

x+2=13/3

Step 2: Subtract 2 from both sides.

x+2−2=13/3−2

x=7/3

Answer:

since the decay rate constant of0.0 250 min.

hence the time required for the sample to decay to one forth of it's initial value is

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

g={(0,1), (2,-6),(4,7),(5,1), (8,1) } its korrect now

Making Vi the subject of formula gives the following expression: Vi = √(Vf² - 2aX).

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

In this exercise, you're required to describe the steps that should be taken to rearrange and make Vi the subject of formula. Therefore, the appropriate and required steps are listed as follows:

Vf² = Vi² + 2aX

Subtracting 2aX from both sides of the equation, we have:

Vf² - 2aX = Vi² + 2aX - 2aX

Vi² = Vf² - 2aX

Taking the square root of both sides, we have:

Vi² = Vf² - 2aX

Vi = √(Vf² - 2aX)

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Step-by-step explanation:

5x-2+3-7

0=5x-9+3

0=5x-6

6=5x

x=6/5

Answer:

0.16 for one egg. 1.90 for a dozen.

Step-by-step explanation:

For 24 eggs it is 3.79 dollars, so to find the price of one egg we just divide 3.79 by 24, which is 0.16.

There are 12 eggs in a dozen, and it's 3.79 for 24 eggs, so I can divide it by 2 to get to a dozen, so 3.79/2 = 1.90

Answer:

.16 per egg

1.90 for a dozen

Step-by-step explanation:

Take the total cost and divide by the number of eggs to find the cost for one egg

3.79/24 =.157916667

Since this is money we round to the nearest cent

.16

The cost per one egg is .16 or 16 cents

Multiply this by 12 to get the cost of 12 eggs

3.79/24  * 12 =1.895

This will round to 1.90

(Do not use the rounded answer to find the cost of a dozen eggs, because it will be higher.  We need to use the exact answer when calculating)

Answer:

1. 13^5

2. prime

3. 8

4. 13

5. 6

The equation for a​ two-week trip of 500 miles' rental cost is Total rent cost = 2x + 500y

Information about the problem:

To solve this problem, we have to state the equation using the information of the problem:

Car rent for 2 weeks = 2x

Car rent for 500 miles = 500y

Total rent cost = 2x + 500y

Example:

Car rent per week = $280/ week

Car rent per miles = $0.75/ mile

Total rent cost = (2 weeks * $280/ week) + (500 miles * $0.75/ mile)

Total rent cost = $560 + $375

Total rent cost = $935

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

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Answer:

Full-time worker minimum monthly income = US$ 7,846.40

Part-time worker minimum monthly income = US$ 7,846.40

Full-time worker hourly wage = US$ 49.04

Part-time worker hourly wage = US$ 98.08

Step-by-step explanation:

1. Let's review the information given to answer the question correctly:

Monthly costs of a 2-adult and 3-children family in the Modesto metro area = US$ 7,846

Full-time worker = 4 weeks of 40-hour per month

Part-time worker = 2 weeks of 40-hour per month

2. Let's calculate the minimum monthly income and hourly wage per worker

Full-time worker hourly wage = Monthly costs/160

Part-time worker hourly wage = Monthly costs/80

Full-time worker hourly wage = 7,846/160

Part-time worker hourly wage = 7,846/80

Full-time worker hourly wage = US$ 49.04

Part-time worker hourly wage = US$ 98.08

Full-time worker minimum monthly income = Hourly wage * 160

Part-time worker minimum monthly income = Hourly wage * 80

Full-time worker minimum monthly income = US$ 7,846.40

Part-time worker minimum monthly income = US$ 7,846.40

Answer:

Step-by-step explanation:

8:12

24:36

Answer:

I would say 6

Step-by-step explanation:

Difference is subtraction.

Answer:

(Choice A) A Yes

Step-by-step explanation:

Answer:

the prime factorizime of 90 is this 2 × 3 × 3 × 5 or 2 × 3² ×5

Answer:

5/2 or 2.5

Step-by-step explanation

Five over two or two and 5 tenths

Answer:

x=-3

Step-by-step explanation:

Let's solve your equation step-by-step.

−7+2(−4x−3)=11

Step 1: Simplify both sides of the equation.

−7+2(−4x−3)=11

−7+(2)(−4x)+(2)(−3)=11(Distribute)

−7+−8x+−6=11

(−8x)+(−7+−6)=11(Combine Like Terms)

−8x+−13=11

−8x−13=11

Step 2: Add 13 to both sides.

−8x−13+13=11+13

−8x=24

Step 3: Divide both sides by -8.

−8x

−8

=

24

−8

x=−3

The orange will fall 64 feet in 8 seconds.

Distance:

Distance is defined as how much ground an object has covered despite its starting or ending point.

Given,

The distance a falling object travels towards the earth is directly proportional to the square of the time that it falls.

And an orange falls 16 feet in 4 seconds.

Here we need to find the how far it will fall in 8 seconds.

Based on the given details,

We know the that distance is,

D = kt²  

where

k is the constant of proportionality.  

To find the value of k we have to apply the given values on the equation.

=> 16 = k x (4)²

=> 16 = k x 16

=> k = 16/16

=> k = 1.

So, in 8 seconds it will fall at

=> D = 1 x (8)²

=> D = 1 x 64

=> D = 64 feet.

Therefore, the orange will fall at 64 feet in 8 seconds.

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Option B) is correct that is shape 2 is congruent to shape 1 because shape 2 is reflection of shape 1.

We know that two figures or objects are congruent if they have the same shape and size or they are the mirror image of each other.

Translation : It simply means moving. Every point should be moved in same distance and in same direction

Rotation : It means turning around a center.

Reflection : In this, the image is of the same size as the pre-image.

So according to the given figure we can see that the shape is not translated or rotated from a center but is reflected as shape 1 is the image of shape 2.

Hence shape 2 is congruent to shape 1 because shape 2 is reflection of shape 1.

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Rita, John, and Kareem sent  17, 7, and 68 messages, respectively.

Use algebraic expressions to solve this problem.

Let x, y, and z be the number of messages sent by Rita, John, and Kareem, respectively.

If Rita, John, and Kareem sent a total of 92 text messages during the weekend, then:

x + y + z = 92

If Kareem sent 4 times as many messages as Rita, then:

z = 4 * x

z = 4x

If John sent 10 fewer messages than Rita, then:

y = x - 10

Evaluating z = 4x and y = x - 10 to the first equation:

x + y + z = 92

x + (x - 10) + 4x = 92

x + x - 10 + 4x = 92

6x = 92 + 10

6x = 102

x = 17

Recall that y = x - 10:

y = 17 - 10

y = 7

And z = 4x:

z = 4(17)

z = 68

If x, y, and z are the number of messages sent by Rita, John, and Kareem, respectively, then Rita, John, and Kareem sent 17, 7, and 68 messages, respectively.

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The length of the side AD after undergoing a dilation using a scale factor of 1.5 as required in the task content is; 16.5.

To evaluate the length of side AD prior to the transformation which involves a dilation.

The distance between two points is given by;

D = √((y2 - y1)² + (x2 x1)²)

It follows that the lengths of the pre-image can be determined as follows;

AD = √((-5-6)² + (5 -5)²)

AD = √(-11)² + 0²

AD = √121

AD = 11

Ultimately, upon undergoing a dilation using a scale factor of 1.5, the length of AD becomes; 11 × 1.5

Hence, AD = 16.5.

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Answer:

£275

Step-by-step explanation:

To find how much Ben's rent is per month, we first have to find how much Ben spends on rent annually (every year). We can do this by multiplying his annual salary by the percentage spent on rent.  

22000 · 0.15 = 3300

Now that we know Ben spends 3300 on rent a year, we can divide that amount by 12 (the number of months in a year) to find out how much his rent is per month.

3300 / 12 = 275

Answer:

The answer is 1

Step-by-step explanation:

The reason the answer is 1 its because 1 its a good number and everybody loves 1

Answer:36

Step-by-step explanation: 36 days

A fort is provided with food for 80 soldiers to last for 60 days. After 15 days, the food is sufficient for 80 soldiers for (60 – 15) days = 45 days. After 15 days, 20 additional soldiers join the fort. = 36 days.

Answer:

Step-by-step explanation:

A fort has food for 80 soldiers to last for 60 days.

Next 15 days the food is for 80 soldiers (60 – 15) days = 45 days.

Next 15 days, 20 MORE soldiers join the fort. = 36

ASNWER: 36 DAYS

Answer:

=-1

Step-by-step explanation:

3x2/2 + -4

6/2 + -4

3 + (-4)

=-1

Answer:

-1

Step-by-step explanation:

Brackets

Indicies

Division

Multiplication

Addition

Subtraction

3 × 2/2 + -4

no brackets. no indicies.

Division

2/2 = 1

3 × 1 + -4

Multiplication

3 × 1 = 3

Addition

3 + -4 = -1

Using the midpoint formula, the coordinates of point U are: (9, 2).

The midpoint formula is: M[(x2 + x1)/2, (y2 + y1)/2]

Given the following:

Midpoint of TU is at: M(5,5)

Point T is at (1, 8), therefore, let:

M(5,5) = (x, y)

T(1, 8) = (x1, y1)

U(?, ?) = (x2, y2)

Plug in the values

M(5, 5) = [(x2 + 1)/2, (y2 + 8)/2]

5 = (x2 + 1)/2

10 = x2 + 1

10 - 1 = x2

9 = x2

x2 = 9

5 = (y2 + 8)/2

10 = y2 + 8

10 - 8 = y2

2 = y2

y2 = 2

The coordinates of point U are: (9, 2).

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