17 Select the correct answer.
What are the solutions of this quadratic equation?
4x² + 3 = 4x + 2

OA. x = 1/ 2
OB. x = -2 ± √3
OC. x = 2
OD. x = 1+√3​

Step-by-step explanation:

gradient = slope or several other words.

it describes how strongly a line (or tangent to a bent curve) is going up or down or ... if it is changing at all.

it is represented by the ratio

(y coordinate change / x coordinate change)

when going from one point on the line to another.

in our case, when going from A to B we have

x changes by -2k (from 3k to k).

y changes by -11 (from 8 to -3).

so, the gradient or slope is

-11/-2k = 3

11/2k = 3

11 = 3×2k = 6k

k = 11/6

A = (33/6, 8) = (11/2, 8)

B = (11/6, -3)

Answer:

1

Step-by-step explanation:

a) Flip the equation

4x - 2 = 2

b) Add 2 to both sides

4x - 2 + 2 = 2 + 2

4x = 4

c) Divide both sides by 4

4x/4 = 4/4

x = 1

From the calculation below, the equivalent to the fraction represented by point M on the number line is [tex]\frac{1}{4}[/tex].

On the number line, it can be observed that there are eight points starting from the first point after 0 up to 1.

Since M is on the second point on the number line, we can have:

P = Point at which M is located on the number line = 2

T = Total number of points on the number line = 8

Therefore, we have:

[tex]M =\frac{P}{T}[/tex]

[tex]M=\frac{2}{8}[/tex]

[tex]M =\frac{1}{4}[/tex]

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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:

629.3 cm3

Step-by-step explanation:

This is known as a rectangular prism aka cuboid.

The formula for the volume is Length x width x height

so 14.5x7x6.2 = 629.3 cm cubed

B(4015) is the [tex]2008^{th[/tex]term of the sequence.

What is the sequence?

Since the mean of the first terms is, the sum of the first terms is n². Thus, the sum of the first 2007 terms is 2007² and the sum of the first 2008 terms is 2008² Hence, the 2008th term of the sequence is

2008² - 2007² = (2008 + 2007) (2008 - 2007) = 4015

Note that n² is the sum of the first n odd integers.

From inspection, we see that the sum of the sequence is n². We also notice that n² is the sum of the first n odd integers.

Because 4015 is the only odd integer, B is the answer.

B(4015) is the [tex]2008^{th[/tex]term of the sequence.

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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:

x<-5/4 or x>2

Step-by-step explanation:

-4x -11 > 5

    +11   +11

-4x>5

/      /

-4   -4   Switch the sign when divided by a negative.

x<-5/4

8x - 7 > 9

    +7   +7

8x>16

/      /

8    8

x>2

Answer:

A) The unit prices are the same.

Step-by-step explanation:

First convert dollars to cents to make the calculation easier

Package of 50 paper plates costs $2.50
$2.50 = 2.50 x 100 = 250¢
So the unit price, which is the price per paper plate = 250/50 = 5¢

Package of 80 paper plates costs $4.00
$4.00 = 4.00 x 100 = 400¢
So the unit price, which is the price per paper plate = 400/80 = 5¢

So the unit prices of both packages are the same

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 area of a sidewalk that surrounds a rectangle of 4 ft by 6 ft  is 56 ft²

The given situation can be depicted in the attached picture.

Recall the formula to calculate the area of a rectangle:

  A = l ⨉ w

Where:

l = length

w = wide

In the attached picture, the area of the sidewalk is the one with green color.

Notice that:

Area of sidewalk = area of bigger rectangle – area of smaller rectangle

Parameters of the bigger rectangle:

l = 6 + 2 + 2 = 10 ft.

w = 4 + 2 + 2 = 8 ft.

Area of bigger rectangle = 10 x 8 = 80 ft²

Parameters of the smaller rectangle:

l = 6 ft.

w = 4 ft.

Area of bigger rectangle = 6 x 4 = 24 ft²

Hence,

Area of sidewalk = 80 - 24 = 56 ft²

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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

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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answer

ex 17

2 3/4 ×8

=11/4×8/1

=11/24

ex 18

9/2× 5/4

=36/10

4

Answer:

he traveled 900 feet

Step-by-step explanation:

250 + 650 = 900

Mr. Carter traveled a total distance of 900 feet from his boat to where he ended up.

Here, we have to find the total distance that Mr. Carter traveled from his boat to where he ended up, we need to calculate the sum of the distances above and below sea level.

The distance above sea level is 250 feet (his house boat's level), and the distance below sea level is 650 feet (where he ended up after jumping).

Total distance traveled = Distance above sea level + Distance below sea level

Total distance traveled = 250 feet + 650 feet

Total distance traveled = 900 feet

Mr. Carter traveled a total distance of 900 feet from his boat to where he ended up.

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The location of the y value of R' after using the translation rule is -10

The translation rule is given as:

(x + 4, y - 7)

The pre-image of R is located at (-17, -3)

Rewrite as

R = (-17, -3)

When the translation rule is applied, we have:

R' = (-17 + 4, -3 - 7)

Evaluate

R' = (-13, -10)

Remove the x coordinate

R'y = -10

Hence, the location of the y value of R' after using the translation rule is -10

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Answer:

exact form: 17/10

decimal form: 1.7

mixed number form: 1  7/10

Step-by-step explanation:

The amount of the discount that was given is $300.

A discount reduces the price of an item. When a discount is given, the item becomes cheaper. VAT is value added tax. VAT increases the price of an item.

The equation that can be used to represent the total cost of the bicycle is:

Total cost after VAT and discount = (1 + VAT) x (marked price - discount)

1921 = (1 + 0.13) x (2,000 - d)

1921 = 1.13 x (2,000 - d)

In order to determine the value of discount, take the following steps:

Divide both sides of the above equation by 1.13

1921 / 1.13 = 2000 - d

1,700 = 2,000 - d

Combine similar terms: 2000 - 1700 = d

Add similar terms together: d = 300

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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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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.

Answer:

nnk;'/mnhjjfn;h;;vhxpycoyyoly,

Step-by-step explanation:

I]o]ogi-gogoig]gogh]o]v]b]bob]b]k k k lgg]goghjppkngghhjjl

No generalizations can be made because the sample size is too small. Therefore, the correct option is option A.

A restaurant is an institution of business which prepares and provides clients with food and beverages. Although many restaurants now provide take-out as well as food delivery services, meals are often served and consumed on the premises.

A restaurant serves breakfast, lunch, and dinner. The restaurant offers a daily special. To estimate the percentage of customers who order the daily specials, the restaurant selected a random sample of customers who had lunch during 2 month period. From the results, the restaurant determined that 25% of these customers ordered the daily special. No generalizations can be made because the sample size is too small.

Therefore, the correct option is option A.

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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

1) Unit Rate of the given options are;

$0.05 for 1 ounce

24 bottles per case

16 ounces per bottle

2) Rate of the given options are;

5 bottles for $5

$1 per 16 ounces

A unit rate (or unit ratio) describes how many units of the first type of quantity corresponds to one unit of the second type of quantity. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second.

Meanwhile, a rate is the ratio between two different units of measure.

Thus;

1) Unit Rate of the given options are;

$0.05 for 1 ounce

24 bottles per case

16 ounces per bottle

2) Rate of the given options are;

5 bottles for $5

$1 per 16 ounces

3) The option that is neither a unit rate nor a rate is; 36 bottles

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The solution to the inequality using William's template is x  > 21.5/19

The inequality expression is given as

-1.5(4x + 1) > 45 - 25(x + 1)

For parentheses: Distribute

So, we have

-6x - 1.5 > 45 - 25x - 25

2. If necessary: Combine Terms

So, we have

19x  > 21.5

3. Apply properties: Divide both sides by 19

x  > 21.5/19

Hence, the solution to the inequality using William's template is x  > 21.5/19

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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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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

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 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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