10. Solve the equation by completing the square. Round to the nearest hundredth if necessary. x²-3x - 3=0
-3.75, 6.75
2.72,0.28
0.87, 2.29
3.79,-0.79

Answer:

1 solution

Step-by-step explanation:

2y + 20y - 15 = 19 + 20y , that is

22y - 15 = 19 + 20y ( subtract 20y from both sides )

2y - 15 = 19 ( add 15 to both sides )

2y = 34 ( divide both sides by 2 )

y = 17

Answer:

Step-by-step explanation:

Answer

one

Proof

2y + 20y - 15 = 19 + 20y             Combine the left side.

22y - 15 = 19 + 20y                      Add 15 to both sides

22y - 15+15 = 19 +15 + 20y          Combine

22y = 34 + 20y                            Subtract 20y from booth sides

22y-20y = 34 + 20y-20y             Combine

2y = 34                                          Divide both sides by 2

2y/2 = 34/2

y = 17

That's the only solution you get. The number of solutions to any equation (with certain exceptions) is the highest power on the variable.

x^2 + 2x - 8    has 2 solutions (from the x^2)

x^3 + 3x^2 + 2x + 15 = y has three solutions

False

• Correlation means that there is a relationship or patter between the two variables. A scatter plot displays the data about the two variables as a set of points in the x-y plane and it is a useful tool for determining if there is a correlation between the variables.

• Causation means the one event causes other event to occur. It can only be determined by designed experiment.

• While correlation and causation both can exist at the same time, correlation doesn’t imply causation.

• Causation explicitly applies only to cases where action P causes outcome Q whereas correlation is simply a relationship.

Correlation doesn’t prove causation.

There could be third variable associated with the size of engine which caused the truck to have greater horsepower. For example, it can be that manufacturers anticipate that consumers who wanted trucks with greater horsepower also prefered trucks with larger engines and therefore chooses to make trucks with larger horsepower.

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Answer:

Part A: 28.26t²

Part B: 2,826 square unit

Explanation:

Part A:  

A[p(t)] = π (3t)² = 3.14 * 9t² = 28.26t²

Part B:

p(10) = 3(10) = 30

A(p) = 3.14 * 30² = 3.14 * 900 = 2,826 square unit

The probability that the number chosen is dividible by 5 or 8 is 0.306.

According to the given question.

A number is chosen at random from the positive even integers from 2 to 50.

Now the total positive intergers from 2 to 50 which are divisible by 5 or 8 are {5, 8, 10, 15, 16, 20, 24, 25,30, 32, 35, 40, 45, 48, 50}

So, there are total 15 positive intergers from 2 to 50 which are divisible by 5 or 8.

⇒ Total number of favourable outcomes = 15

And the total positive integers from 2 and 50 is 49.

⇒ Total number of outcomes is 49.

As we know that, proabability is calculated by taking the ratio of favourable outcomes to the total number of outcomes.

Therefore, the probability that the number chosen is divisible by 5 or 8

= 15/49

= 0.306

Hence, the probability that the number chosen is dividible by 5 or 8 is 0.306.

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Answer:

Okay so a couple key points

$5.00 to ship it

Postcard stamps = $0.34

First class stamps= $0.49

And lastly he has 7 first class stamps

So with that being said you take .49 and times it by 7 since he has seven of them and that would be $3.43

And now you take $3.49 and subtract it from the $5.00 you'd be left with $1.57

Now you take $.34 and divide it by $1.57 and you would get a total of 4.61 so that means you would need five postcard stamps

So to be able to ship the package you'd need 7 first class stamps and 5 postcard stamps

Answer:

25 students and 40%

Step-by-step explanation:

The expression 1/4x³y + 3/4xy² can be rewritten as: A. 1/4xy(x² + 3y).

We can rewrite an expression by using a factor that is common in an expression.

Given the expression, 1/4x³y + 3/4xy², the common factor in the expression that we can factor out is 1/4xy.

To rewrite the expression, we have the following:

1/4xy into 1/4x³y will give us x²

1/4xy into 3/4xy² will give us 3y.

This will give us:  1/4xy(x² + 3y).

Therefore, the expression 1/4x³y + 3/4xy² can be rewritten as: A. 1/4xy(x² + 3y).

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Answer:

A. one fourth times x times y times the quantity x squared plus 3 times y end quantity

Step-by-step explanation:

Hope this helps you :)

The two methods for estimation of the quotient of 538 divided by 96 is being explained.

We are given that:

538 ÷ 96

We need to estimate the quotient of 538 ÷ 96 by using two methods.

The first method can be that we first estimate the divisor and the dividend to the nearest tens and then perform the division.

538 will be rounded off to 540 and 96 will be rounded off to 100.

So, it becomes:

540 ÷ 100

= 5.4

This will again be rounded off to 5

= 5

The second method will be that we first perform the division and then round off.

538 ÷ 96 = 5.61

Rounding off, we will get:

= 6.

Therefore the two methods for estimation of the quotient of 538 divided by 96 is being explained.

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Answer:

what you have to do is multiply 2 times 4 which is 8 and multiply the 8 by 9 which is 72

Step-by-step explanation:

2*4 =8

8*9=72

72 plus 8 is 80

Answer:

Rise is 4

Run is 5

Slope is 4/5

Step-by-step explanation:

The 2 points on the line (4,-3) and (9,1)

Rise is 4

Run is 5

Slope is 4/5

Answer:

84:56

Step-by-step explanation:

a:b:c

(7:8)

( 12:7)

Answer:

A:C = 3:2

Step-by-step explanation:

A:B = 7:8 is a proportion relationship and can be represented using fractions:

[tex]\displaystyle{\frac{A}{B} = \frac{7}{8}}[/tex]

Similarly the proportion relation B:C = 12:7 can be represented as:
[tex]\displaystyle{\frac{B}{C} = \frac{12}{7}}[/tex]

Multiply the first equation by the second
[tex]\displaystyle\frac{A}{B}\;\mathsf{x}\;\frac{B}{C} = \frac{7}{8}\;\mathsf{x}\;\frac{12}{7}[/tex]

This evaluates to
[tex]\displaystyle\frac{A}{C} = \frac{12}{8}[/tex]

Simplifying gives us
[tex]\displaystyle\frac{A}{C} = \frac{3}{2}[/tex]

So A:C = 3: 2

Based on the calculation below, the rate at which the weeds grow each day is 0.7%.

Given:

f(x) = 3(1.05)x = 3(1 + 0.05)x ................... (1)

Since there are 7 days in a week, the rate at which the weeds grow each day can be calculated from equation (1) by dividing 0.05 (i.e. 5% weekly growth rate) as follows:

f(x) = 3(1 + (0.05 / 7))x

f(x) = 3(1 + 0.007)x

f(x) = 3(1.007)x

Since 0.007 is the same as 0.7%, this implies that the rate at which the weeds grow each day is 0.7%.

The correct option is "f(x) = 3(1.007)7x; spreads at a rate of approximately 0.7% daily".

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Answer: Option 1

Step-by-step explanation: Correct for my test.

In 3 hours Tom drives 243 miles.

So, to find how many miles Tom can drive in 3 hours:

Given: Tom drives 81/2 miles every 1/30 hour.

So, in 30 minutesTom drives 40.5 miles.

Therefore, Tom drives 243 miles in 3 hours.

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answer

ex 17

2 3/4 ×8

=11/4×8/1

=11/24

ex 18

9/2× 5/4

=36/10

4

We get that, the digit is in the 3rd place (hundreds).The difference between the numbers is 500.

We want to change the digit in the number 5,341 into 5,841.

We also need to find the difference between the numbers.

The number 3 is in the 3rd place (hundreds) of the number 5,341 as a digit will be replaced by 8  to form the number 5,841.

This means that 300 is replaced by 800 because the third place in both the numbers is of hundreds.

The difference between 800 and 300 is:

800 - 300 = 500.

Subtraction of 5,341 from 5,841 also yields 500.

Therefore, we get that, the digit is in the 3rd place (hundreds).The difference between the numbers is 500.

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The temperature change in Anchorage,Alaska, each hour is; -11°F per hour

When we talk of rate of change with respect to two values, we simply mean the rate of change of the output value with respect to the input value.

Now, we are told that the temperature went from 0°F to -44°F over a four hour period. Thus;

Rate of change = Change in temperature/change in time

Thus;

Rate of change = (-44 - 0)/(4 - 0)

Rate of change = -44/4

Rate of change = -11°F per hour

The temperature change in Anchorage,Alaska, each hour is; -11°F per hour

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Based on the predicted value, the explanatory variable, and the y-intercept, the value of the slope for Jean's project is C. -1.5

A linear regression equation takes the form of:

y = mx + c

y = predicted value

m = slope

x = explanatory variable

c = y-intercept

Given these values, the slope:

8 = 12m + 26

12m = 8 - 26

m = -18 / 12

m = -1.5

In conclusion, option C is correct.

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Answer: 17 times

Step-by-step explanation:

It takes 6 times for the first recipe (.25x6=1.5)

It takes another 11 times for the second recipe (.25x4=2 + .25x3 = 0.75)

You add 6 + 11 and get 17

Required probability = 120 * 0.0010819 =  0.1298

total number of outcomes of 7 from 10 = 10*9*8 / 3*2*1  = 120

probability of each outcoe is 0.85^7* (0.15)^(3)  = 0.0010819

Required probability = 120 * 0.0010819 =  0.1298

Probability is simply how likely something is to happen.

Whenever we’re unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

The best example for understanding probability is flipping a coin:

There are two possible outcomes—heads or tails.

What’s the probability of the coin landing on Heads? We can find out using the equation P(H) = ?P(H)=?P, left parenthesis, H, right parenthesis, equals, question mark.

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The average of the other 3 numbers is 72.

Average or mean is a measure of central tendency which calculates the central point of a data-set.

Average of a set of numbers is calculated by taking the sum of the numbers and dividing it by the total frequency of the numbers.

If 3 numbers a , b and c are taken then the average is equal to

(a+b+c) ÷3

Given average of 5 numbers is 72.

Therefore the sum of the numbers is  72 × 5 = 360

Two of the numbers are 70 and 74 .

Sum of the remaining 3 numbers = 360 - (70 + 74) = 360 - 144 = 216

Average of the 3 numbers = 216 ÷ 3 = 72

Therefore the average of the remaining 3 numbers is 72.

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The required equation is 4x+6=18.

Option (B) is correct.

A part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.

Given:

Let the number be 'x'

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign.

We have to find the equation..

According to given question we have

i.e

four times a number=4*x

'six more than=4x+6

equals 18'=18

i.e

4x+6=18

Therefore, the required equation is 4x+6=18.

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The equation 2⁻³ = 0.125 in logarithmic form is -3log(2) = log(0.125)

An equation is an expression that shows the relationship between two or more numbers and variables.

A variable can either be dependent or independent. A dependent variable depend on other variable while an independent variable does not depend on other variables.

Given the equation:

2⁻³ = 0.125

Taking the logarithm of both sides:

log(2⁻³) = log(0.125)

-3log(2) = log(0.125)

The equation 2⁻³ = 0.125 in logarithmic form is -3log(2) = log(0.125)

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(a) Slope of AB =    and Slope of CD =

(b) True, both segments are not parallel as they lie on the same line

(c) Distinct lines are the words in Parallel slope property that addresses the problem in part(b).

What is Slope of a line and Parallel Slope Property and co-linear points?

Slope of a line :Given are two points P (x₁, y₁) and Q ( x₂, y₂)

Then slope of the line  PQ is given by  [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

Given Parallel Slope Property: Two  distinct lines are parallel if the have the same slope

Colinear points: A,B,C,D are collinear points if the slopes of lines AB, BC,CD,DA are all equal.

Given the points A(-5,-2), B(1,1), C(-1,0), and D(3,2).

Slope of the line AB [tex]=\frac{1-(-2)}{1--(5)}=\frac{3}{6} =\frac{1}{2}[/tex]

Slope of the line CD [tex]=\frac{2-0}{3-(1)}=\frac{2}{4} =\frac{1}{2}[/tex]

Slope of the line BC [tex]=\frac{0-1}{-1-1}=\frac{-1}{-2} =\frac{1}{2}[/tex]

Slope of the line DA=[tex]\frac{-2-2}{-5-3}=\frac{-4}{-8} =\frac{1}{2}[/tex]

Therefore A,B,C,D are collinear means they lie on the same lines

Slopes of AB and CD are equal but still they  are not parallel because according to Parallel Slope Property two lines with same slope are parallel only when they are distinct but AB and CD are on same line.

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Answer:

exact form: 17/10

decimal form: 1.7

mixed number form: 1  7/10

Step-by-step explanation:

With the help of Pythagoras Theorem for triangles, we get that the possible areas of the square are: 12 sq. units and 20 sq. units, according to the cases mentioned.

According to the Pythagoras Theorem, in a right angled triangle, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Given:

Sides of a right triangle are 2 and 4 units.

To find: Area of a square that shares a side with the third side of the triangle.

Finding:

There can the following cases:

If 2 and 4 units are the lengths of the perpendicular sides.

Then, by Pythagoras Theorem, -

[tex]H^{2} = 2^{2}+4^{2}\\ H^{2} = Side^{2}\\H=Side \\H= \sqrt{4+16} \\H= \sqrt{20} \\H= 2\sqrt{5}[/tex]

Hence, the area of the square = side² = 20 units²

If 4 units is the length of hypotenuse.

Then, by Pythagoras Theorem,

[tex]4^{2} = 2^{2} + A^{2} \\16 - 4 = A^{2} \\= \sqrt{12}\\[/tex]

side of triangle = [tex]\sqrt{12}[/tex]

Hence, the area of the square = side² = 12 units²

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The option that describes the best decision for Larry is Larry buys the second lawn mower because he thinks the extra $5 are worth not having to do the assembly.

The cost of the first lawnmower after the discount is:

= 275 x (1 - 20%)

= 275 x 0.80

= $220

The cost of the second lawnmower is:

= 299 x 0.75

= $224.25

The difference between the lawnmowers is around $5. This $5 is the cost of the assembly on the second lawnmower and Larry might decide that this cost is worth it.

Options for this question include:

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Based on the price of the current model of a sports car, the price increase for the next model will be $1,564

The price of the next model of the sports car will be $35,564.

The increase in price in dollar terms for the next model of the sports car can be found by the formula:
= Current cost of current model x Price increase in percentage

= 34,000 x 4.6%

= $1,564

The price of the next model is therefore:

= Current price of current model + Price increase

= 34,000 + 1,564

= $35,564

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The two such x-values are 2 and 8.

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