Which of the following statements about the product of 3–√2 and 75−−√ is true?

The equation in standard form is D. 4x² - 17x-9=0

To make an equation into standard form is to equate the terms and factors to zero.

Given the expression;

-3x² + 4(x - 2) = 7x(3 - x) + 1

expand the bracket

-3x² + 4x - 8 = 21x - 7x² + 1

Now, collect the like terms

-3x² + 7x² + 4x - 21x = 1 + 8

Add or subtract the like terms

4x² - 17x = 9

Equate equation to zero, we get;

4x² - 17x - 9 = 0

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Five packets of marshmallows cost £4. 80. Then, eight packets of marshmallows cost £7.68.

The problem states that five packets of marshmallows cost £4.80. We need to find out how much eight packets of marshmallows will cost.

To solve the problem, we can use the concept of proportionality. If we assume that the cost of marshmallows is directly proportional to the number of packets, then we can set up a proportion between the cost of five packets and the cost of eight packets.

The proportion can be written as follows:

5 packets / £4.80 = 8 packets / x

where x is the cost of eight packets.

To solve for x, we can cross-multiply the proportion and simplify:

5 packets x = £4.80 x 8 packets

5x = £38.40

x = £38.40 / 5

x = £7.68

Therefore, eight packets of marshmallows will cost £7.68.

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Answer:

Step-by-step explanation:

10

Answer:

Not Possible

Step-by-step explanation:

No answer choices are shown however, we can solve for some that are equivalent so we know which ones are not.

Here are some that are equivalent:

20(2+1)

2(20+10)

40+20

60

Answer:

Let the number of $2 notes be x, while that of $10 notes be y.

Set two equations

x + y = 21     y = 21 - x ------- 1

2x + 10y < 110  ------ 2

Sub 1 into 2

2x + 10(21-x) < 110

2x + 210 - 10x < 110

-8x < -100

x > 12.5

Minimum number of $2 notes in the envelope = 13

Answer:

The length is [tex]9[/tex] inches and the width is [tex]30[/tex] inches.

Step-by-step explanation:

The perimeter of the rectangle is [tex]2x + \frac{4x}{3} = 30[/tex]. We multiply [tex]3[/tex] by both sides which will give us [tex]6x + 4x = 90[/tex]. Adding, we have [tex]10x = 90[/tex]. Dividing [tex]10[/tex] by both sides will give us [tex]x = 9[/tex]. The length of the rectangle is [tex]9[/tex], and the width is [tex]\frac23 \cdot 9 = 6.[/tex] Checking our answer, we have [tex]6 + 6 + 9 + 9 = 30.[/tex] Therefore, the length of the rectangle is [tex]\boxed{9 \text{ inches}}[/tex] and the width of the rectangle is [tex]\boxed{30 \text{ inches}}[/tex].

Hope that helps!

The properties justify the steps are taken to solve the system 2a+7b=0 3a-5b=31 as Multiplication, Substraction, Division,  Simplify, etc.,

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.

'The properties that justify the steps taken to solve the system 2a + 7b = 0, 3a - 5b = 31 are:

2a + 7b = 0, 3a - 5b = 31

10a + 35b = 0, 21a - 35b = 217   <-------> Multiplication property of equality.

31a = 217                                      <-------> Substraction property of equality.

a = 7                                            <-------> Division property of equality.

2(7) + 7b = 0,                             <-------> Substitution property of equality.

14 + 7b = 0,                              <-------> Simplify  

7b = -14,                                   <-------> Simplify  

b = -14/7,                                  <-------> Division property of equality.

b = -2

Therefore, the properties justify the steps are taken to solve the system 2a+7b=0 3a-5b=31 as Multiplication, Substraction, Division,  Simplify, etc.,

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Students raised $225 in the first week and $90 in the second week.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, a student club has a goal to raise $750 to buy new books for a library.

In the first week, the club raised 30% of its goal.

Now, 30% of 750

= 30/100 ×750

= 3×75

= $225

In the second week, the club raised 12% of its goal.

Now, 12% of 750

= 12/100 ×750

= 0.12×750

= $90

Hence, students raised $225 in the first week and $90 in the second week.

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Answer:

-19 > k

Step-by-step explanation:

-4 > k + 15

Subtract 15 from each side.

-4-15 > k + 15-15

-19 > k

Any value less than -19 would make this statement true

Answer:

- 19 > k

Step-by-step explanation:

- 4 > k + 15

Subtract 15 from both sides.

- 4 - 15 > k

- 19 > k

Answer:

Step-by-step explanation:

The interest rate of 1.25% compounded monthly means that the interest earned each month is 1.25% of the current balance. Here's how you can calculate the final balance in the account after 20 years:

First, calculate the interest earned each month: $200 * 1.25% = $2.50

Then, add the interest earned to the monthly deposit to get the new balance: $200 + $2.50 = $202.50

Repeat this process for 240 months (20 years x 12 months/year).

The final balance in the account after 20 years would be approximately $71,934.24.

To find the total money you will put into the account, simply multiply the monthly deposit by the number of months: $200 * 240 = $48,000.

To find the total interest earned, subtract the initial deposit from the final balance: $71,934.24 - $48,000 = $23,934.24

So, in 20 years, you will have put a total of $48,000 into the account, and you will have earned a total of $23,934.24 in interest.

The area and perimeters of the shapes are: (1) Area = 702 ft², perimeter = 96 ft (2): Area = 20 in² Perimeter = 21 in

Perimeter is the distance round the object while the area is the floor space the object occupies

1) Area =  (l*w) + (L*W)

Area = (6*9)  + (24*27)

Area = 54 + 648

Area = 702 ft²

ii) perimeter = 24+27+30+9+6= 96 ft

2)  Area =  (l*w) + (L*W)

Area = (2*3) +( 7*2)

Area = 6+14 = 20 in²

ii) perimeter =2+7+2+2+3+2+3 = 21 in

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The solution to the equation 3x2 - 30x - 72 = 0 is x = -4 and x = -12.

3x2 - 30x - 72 = 0

3x2 - 30x = 72

3x2 - 24x = 90

3x2 - 24x + 18x = 90 + 18x

3x(x - 8) = 108

x(x - 8) = 36

x = 36 or x = 8

x = -12 or x = -4

The equation 3x2 - 30x - 72 = 0is a second-degree polynomial equation with two solutions. To solve this equation, first use the distributive property to factor out 3x from the first two terms. This yields 3x(x - 8) = 108. Then divide both sides of the equation by 3 to get x(x - 8) = 36. From here, use the quadratic formula to solve for x. This yields x = 36 or x = 8. Since the equation was given in terms of x2, the two solutions are x = -12 and x = -4. To confirm this, substitute these values into the original equation and check that it is true.

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Answer: Demographic republic of Congo, Uganda and Gabon

The term "difference" os the result of subtracting one number from another.

So in other terms you want to know what would be the result of subtracting -4.6 from 13.5 :

13.5 - -4.6 = Difference between the two temperatures

Two minus signs turn into a positive sign so :

13.5 - -4.6 =

13.5 + 4.6 =

18.1 = Difference between the two temperatures

Your answer is : The difference between the two temperatures is 18.1

The expression for f(x) - g(x) - h(x) is 6x - 5x² + 6.

Option C is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = 3x + 5

g(x) = 4x² - 2

h(x) = x² - 3x + 1

Now,

f(x) - g(x) - h(x)

= 3x + 5 - (4x² - 2) - (x² - 3x + 1)

= 3x + 5 - 4x² + 2 - x² + 3x - 1

= 6x - 5x² + 6

Thus,

6x - 5x² + 6 is the expression.

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The equation of the total cost is C = 3 + 5x and the amount earned after 5 hours is $28.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

Let us suppose the number of hours = x.

The cost of additional hour is $5.

The cost of x hours is 5x.

Given that, Nicole charges a flat fee of $3, plus $5 per hour.

C = 3 + 5x

If she baby sits for 5 hours, that is x = 5, then:

C = 3 + 5(5)

C = 3 + 25

C = $28

Hence, the equation of the total cost is C = 3 + 5x and the amount earned after 5 hours is $28.

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Answer:

7

Step-by-step explanation:

35-8-4-2=21

21/3=7

Answer:

7 pounds

Step-by-step explanation:

8+4+2=14

35-14=21

21/3=7

To calculate the probability that the first heart it detects with muscle damage is the 8th image geometric distribution should be used.

According to the question medbiz develops and sells medical imaging devices. they are developing a computer program that reads heart images and detects heart muscle damage.

Machine has success rate of 90%

Number of images of hearts with muscle damage = 100

To calculate the probability that the first heart it detects with muscle damage is the 8th image, geometric distribution should be used because  

Geometric distribution is a type of discrete probability distribution that represents the probability of the number of successive failures before a success is obtained in a Bernoulli trial. A Bernoulli trial is an experiment that can have only two possible outcomes, ie., success or failure

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The question is incomplete, the following question is complete:

MedBiz develops and sells medical imaging devices. They are developing a computer program that reads heart images and detects heart muscle damage. Early studies show the machine has a 90% success rate. The programs is shown 100 images of hearts with muscle damage. What distribution should be used to calculate the probability that the first heart it detects with muscle damage is the 8th image?

binomial distribution

geometric distribution

hypergeometric distribution

none of the other choices

The value of x in the equation is 8 or -27

The exponential function is a mathematical function denoted by f(x)=\exp or e^{x}. Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex.

X^2/3 + X^1/3 -6 = 0

= X^1/3(2) + X^1/3 -6 = 0

represent X^1/3 by K

= K²+k-6 = 0

(K +3k )(-2k -6)= 0

k(3+k) -2(k+3) = 0

(k+3)(k-2) = 0

k+3 = 0

k -2 = 0

k = -3 or 2

since K = x^1/3

when k =-3

-3 = x^1/3

x = -3³ = -27

when k = 2

x = 2³ = 8

therefore the value of x is -27 or 8

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Answer:x=251

Step-by-step explanation:

Step 1: Subtract 8 from both sides of the equation.

Explanation: Subtracting 8 from both sides of the equation keeps the equality balanced.

Step 2: x = 251

Explanation: Subtracting 8 from both sides of the equation gives us

x = 259 - 8 = 251.

Answer:

Step-by-step explanation:

x = -251

The possible values of the length of the rectangle is x > 34, the correct option is A.

For a rectangle with length and width L and W units, we get:

Area of the rectangle = [tex]L \times W \: \rm unit^2[/tex]

Perimeter of the rectangle = [tex]2(L + W) \: \rm unit[/tex]

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

Given that width is 8 inches less than the length x

Sum of length and width more than 60

Now, the length is x

Width is x-8

x-8+x>60

2x>60

x>30

Therefore, the length of rectangle will be  x > 34

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The probability the math majors are seated together is 0.028 and all seated togeather with their group is 0.0047.

Probability is the probability that something will happen. Whenever the outcome of an event is uncertain, we can speak of the probability, or likelihood, of a particular outcome. Analyzing events according to their probabilities is called statistics.

Probability determines the likelihood of an event occurring.

P(A) = f / N. Odds and probabilities are related, but odds depend on probabilities. Before we can determine the probability that an event will occur, we first need the probability.  

total number of teacher is 10

so number of ways total 10 teacher seat = 10!/(6!*4!)

= 210

and

the number of ways  the math majors are seated together

= 6

probability = 6/210 = 0.028

the number of ways the math majors are seated together and the computer science majors are seated together

= 1

probability = 1/210

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Answer:

The first term is, x2 its coefficient is 1 .

The middle term is, -9x its coefficient is -9 .

The last term, "the constant", is +16

Step-1 : Multiply the coefficient of the first term by the constant 1 • 16 = 16

Step-2 : Find two factors of 16 whose sum equals the coefficient of the middle term, which is -9 .

-16 + -1 = -17

-8 + -2 = -10

-4 + -4 = -8

-2 + -8 = -10

-1 + -16 = -17

1 + 16 = 17

2 + 8 = 10

4 + 4 = 8

8 + 2 = 10

16 + 1 = 17

The equivalent to the ratio 1:2 is 2 : 4

From the question, we have the following parameters that can be used in our computation:

Ratio = 1 : 2

To determine the equivalent expression, we multiply each proportion of the ratio by the same number (say 2)

Using the above as a guide, we have the following:

Ratio = 2 * 1 : 2 * 2

Evaluate

Ratio = 2 : 4

Hence, the ratio is 2 : 4

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Each week, Desiree earns $925 and pays $149 in payroll tax it will take Desiree at least 4 weeks to earn at least $3000 after taxes.

What is Gross earning ?

Gross earnings refer to the total amount of money that an individual earns before any deductions are taken out. These earnings can include regular salary or wages, as well as any bonuses, tips, or commissions that are earned. Gross earnings are usually reported on a paycheck or pay stub, and may be subject to various taxes and other deductions.

Desiree's net earnings after payroll tax can be calculated by subtracting the tax amount from her gross earnings:

Net Earnings = Gross Earnings - Payroll Tax

Net Earnings = $925 - $149

Net Earnings = $776

To earn at least $3000 after taxes, Desiree needs to earn a total of:

Total Earnings = $3000 + Payroll Tax

Total Earnings = $3000 + $149

Total Earnings = $3149

We can now set up an equation to solve for the number of weeks, x, it will take for Desiree to earn at least $3149:

Net Earnings per week * Number of Weeks = Total Earnings

$776 * x = $3149

Solving for x:

x = $3149 / $776

x = 4.05

Therefore, it will take Desiree approximately 4.05 weeks to earn at least $3000 after payroll tax. Since you can't earn partial weeks, we can round up to 5 weeks to ensure that Desiree has earned at least $3000.

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The expression can be written as the trinomial below.

3x2 - 14x + 15

Here we just need to expand the expression:

(x - 3)*(3x - 5)

Just expanding that product we will get:

(x - 3)*(3x - 5)

x*(3x) - 3*(3x) + x*(-5) - 3*(-5)

3x^2 - 9x - 5x + 15

3x2 - 14x + 15

So we have 3 terms now, thus, this is a trinomial.

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Answer:

32 markers

Step-by-step explanation:

Ty has 8 x 3 = 24 markers.

Together, they have 8 + 24 = 32 markers.

Answer:

0.75

Step-by-step explanation:

The slope-intercept form is one way to write a linear equation (the equation of a line). The slope-intercept form is written as y = mx+b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis).

Answer:

the slope is -6/-5