Find the value of X.

Answer:  the number that can be placed in the box to make the statement true is 3.

Step-by-step explanation:

To make the statement true, we need to find a number that, when added to 7, equals 10. From the given options, the number that satisfies this condition is 3.

If we substitute 3 for the box in the statement, it becomes:

If +7=10, then 10-7=3.

The polynomial whose zeroes are 2α+1 and 2β+1 is determined as x² - 4x - 5 = 0.

The zeros of the quadratic polynomial is calculated by applying the following formula as follows;

The given polynomial function;

f(x) = x²  -  x  - 2

The zeros of the quadratic polynomial is calculated as;

let x = - 1

f(-1) = (-1)² - (-1) - 2

f(-1) = 1 + 1 - 2

f(-1) = 0

So α = - 1

Let x = 2;

f(2) = (2²) - 2 - 2

f(2) = 4 - 4

f(2) = 0

so β = 2

The value of 2α + 1 is calculated as;

2α + 1 = 2(-1) + 1 = -1

The value of 2β + 1 is calculated as;

2β + 1 = 2 (2) + 1 = 5

x = -1 or x = 5

x + 1 = 0 or x - 5 = 0

(x + 1)(x - 5) = 0

x² - 5x + x - 5 = 0

x² - 4x - 5 = 0

Thus, the polynomial whose zeroes are 2α+1 and 2β+1 is determined as x² - 4x - 5 = 0.

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The area of the triangle, when a = 2 and c = 3, is 1512 square centimeters.

We must apply the formula for the area of a triangle, which is provided by: to determine the triangle's area.

(1/2) * Base * Height = Area

We can enter the values of a = 2 and c = 3 into the formula given that the base length is 3ac2 and the height is 2 centimetres greater than the base length.

Base length =[tex]3ac^2 = 3 * 2 * (3^2) = 3 * 2 * 9 = 54[/tex] centimeters

Height is calculated as Base Length + 2 (54 + 2 = 56 centimetres).

Using these values as a substitute in the formula, we obtain:

Area =[tex](1/2) * 54 * 56 = 1512[/tex] square centimeters

centimetres square

It's crucial to understand that the calculation assumes the triangle is a right triangle with the specified base and height and that the given values of a and c are accurately used in the formula.

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The two functions f and g are f(x) = 5/x² and g(x) = 9x + 6

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

(f o g)(x) = 5/(9x + 6)²

The function (f o g)(x) can be calculated using

(f o g)(x) = f(g(x))

This means that we can set the denominator of (f o g)(x) = 5/(9x + 6)² to g(x)

So, we have

g(x) = 9x + 6

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

(f o g)(x) = 5/(g(x))²

So, we have

f(x) = 5/x²

Hence, the two functions f and g are f(x) = 5/x² and g(x) = 9x + 6

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The expression is solved to give 93 1/3

Fractions are defined as the part of a whole element, a whole number or a whole variable.

In mathematics, there are different types of fractions.

The types of fractions are listed as;

From the information given, we have that the fraction is;

140/1.5

Convert 1.5 to fraction, we have;

1.5 = 3/2

Substitute the value, we have;

140/3/2

Then, we get;

140(2)/3

Multiply the values, we get;

93  1/3

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(a) The  square of 4 = 16

(b) The  square of 6 = 36

(b) The  square of 13 = 139

(b) The  square of 10 = 100

We know that,

Square of a number is nothing but product of a number with itself.

And it gives power  2.

(a) Now the given number is 4:

The  square of 4 = 4²

                            = 4x4

                            = 16

(b) The given number is 6:

The  square of 6 = 6²

                            = 6x6

                            = 36

(c) The given number is 13:

The  square of 13 = 13²

                            = 13x13

                            = 139

(d) The given number is 10:

The  square of 10 = 10²

                            = 10x10

                            = 100

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Given statement solution is :- It  would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.

To find the cost of installing tile in the dining room and carpet in the bedroom, we need to calculate the areas of both rooms first.

Given:

Every 2 centimeters on the floor plan represents 1 meter of the house.

Dining Room:

On the floor plan, the dining room is 8 cm by 10 cm.

Converting this to meters, the dimensions of the dining room are 8 cm / 2 = 4 meters by 10 cm / 2 = 5 meters.

The area of the dining room is 4 meters * 5 meters = 20 square meters.

Bedroom:

On the floor plan, the bedroom is 6 cm by 10 cm.

Converting this to meters, the dimensions of the bedroom are 6 cm / 2 = 3 meters by 10 cm / 2 = 5 meters.

The area of the bedroom is 3 meters * 5 meters = 15 square meters.

Now, let's calculate the costs.

Cost of Tile:

The cost of installing tile is $34 per square meter.

The area of the dining room is 20 square meters.

Therefore, the cost of installing tile in the dining room is 20 square meters * $34/square meter = $680.

Cost of Carpet:

The cost of installing carpet is $21 per square meter.

The area of the bedroom is 15 square meters.

Therefore, the cost of installing carpet in the bedroom is 15 square meters * $21/square meter = $315.

Therefore, it would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.

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In Container B, there are roughly 1.7643 kg of sand.

Compared to Container B, Container C had about 0.7057 kg less sand.

Let's say that Container B contains 'x' kilogrammes of sand.

The amount of sand in Container A is 2x kg since it has twice as much as Container B does.

The amount of sand in Container C grew by 20% after 15% of the sand from Container A and 20% of the sand from Container B were transferred there.

Let's figure out how much sand is in Container C:

Sand moved from Container A to Container C weighed 0.15 x 2 x kg.

The amount of sand moved from Container B to Container C is equal to 0.20 * x kg.

After the transfer, Container C now contains 20% more sand overall. Sand in Container C therefore contains 1.2 times as much as it did initially.

After the transfer, the total amount of sand in Container C is equal to 1.2 * (0.3x + 0.2x) = 1.2 * 0.5x = 0.6x kg.

Therefore, we can conclude that Container C held 2.47 kg more sand than Container A. Thus, we can construct the following equation:

0.6x - 2x = 2.47

Simplifying the equation:

-1.4x = 2.47

Dividing both sides by -1.4:

x = -2.47 / -1.4 ≈ 1.7643

So there is roughly 1.7643 kg of sand in Container B.

To determine the variation in sand content between Containers C and B:

Sand in Container C less Sand in Container B equals the difference.

Difference = 0.6x - x

Difference = -0.4x

Substituting the value of x:

Difference = -0.4 * 1.7643 ≈ -0.7057

Container C therefore contained around 0.7057 kg less sand than Container B.

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The value of x, considering the similar triangles in this problem, is given as follows:

x = 3.6.

Similar triangles are triangles that share these two features listed as follows:

The proportional relationship for the side lengths in this problem is given as follows:

3/20 = x/24

Applying cross multiplication, the value of x is obtained as follows:

20x = 72

x = 72/20

x = 3.6.

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Answer:

156 cm²

Step-by-step explanation:

The surface area of a square pyramid is a² + 2al if a = the length of the side of the base of the pyramid and l = the height of each triangle. a would be equal to 6 in this case, since it is the length of the side of the base, and l would be 10 because it is the height of each triangle.

So, here's our expression:

6² + 2(6)(10) =

36 + 12(10) =

36 + 120 =

156

The surface area of the square pyramid is 156 cm². If this process doesn't make sense to you or if you'd like some further clarification, please let me know! :)

The total amount paid in the first month would be $32 for the minimum payment plus $9.20 for the interest, totaling $41.20.

If you have a credit card with an annual percentage rate (APR) of 30% and a minimum payment requirement of 8% of the balance, and you have a balance of $400 on the credit card, you decide to stop charging and pay it off by making the minimum monthly payment each month, here's how it would work:

The minimum monthly payment would be 8% of the balance, which is 0.08 x $400 = $32.

Each month, you would make a payment of $32 towards your credit card balance. However, keep in mind that the interest will continue to accrue on the remaining balance.

Since the APR is 30%, the monthly interest rate would be 30% / 12 = 2.5%.

To calculate the interest charged each month, you multiply the remaining balance by the monthly interest rate. For example, after the first payment, the remaining balance is $400 - $32 = $368. The interest charged for that month would be 2.5% x $368 = $9.20.

Therefore, the total amount paid in the first month would be $32 for the minimum payment plus $9.20 for the interest, totaling $41.20.

Each month, you would continue making the minimum payment, and the interest charged would be based on the remaining balance. The process would continue until the balance is paid off in full.

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The length of the longer leg (the other leg) is 9 units.

Let's denote the length of the shorter leg of the right trapezoid ABCD as 'a' and the length of the longer leg as 'b'. We can set up the following equations based on the given information:

Area of the first shaded triangle = Area of the second shaded triangle + 54 sq units

(1/2) * a * b = (1/2) * (a + 12) * b + 54

Simplifying equation 2:

a * b = (a + 12) * b + 108

ab = ab + 12b + 108

0 = 12b + 108

12b = -108

b = -108 / 12

b = -9

Since length cannot be negative, we discard the negative solution. Therefore, the length of the longer leg (the other leg) is 9 units.

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Answer:

6(4c-3), 9w-1

Step-by-step explanation:

GCF is the biggest thing you can divide both 24c and 18 by.

you can see that you can divide both 24c and 18 by 6, and when you do that you get 4c and 3. That means that the answer for that question is

6(4c-3)   (which is A)

The next question all you need to do first is distribute the 3/4 to the 12w and 8.

3/4 * 12w = 9w

3/4 * 8 = 6

so you get

9w -6 + 5

you combine like terms to get

9w - 1  (B)

Answer:

Step-by-step explanation:

The correct option for the approximate value of [tex]\sf -12 + \sqrt{32}[/tex]  is -6.3 to the nearest tenth.

An approximation is anything that is similar, but not exactly equal, to something else.

The given expression is:

[tex]\sf -12 + \sqrt{32}[/tex]

The value of [tex]\sqrt{32}[/tex] is given as 5.656

Since, after decimal 6 to the right of 5 is greater than 5

To the nearest tenth, we can write as 5.66

[tex]\sf \therefore \sqrt{32} = 5.66[/tex]

For the required value of the expression we can write,

[tex]\sf -12 + \sqrt{32}[/tex]

Put the value of [tex]\sf \sqrt{32} = 5.66[/tex]

Putting values in expression we have,

[tex]\sf -12 + \sqrt{32} = -12 + 5.66[/tex]

Solving them

[tex]\sf \rightarrow -12 + \sqrt{32} = -6.34[/tex]

Hence, the approximate value of [tex]\sf -12 + \sqrt{32}[/tex] is -6.3 to the nearest tenth.

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The amount of money Brooklyn need to invest, for the value of the account to reach $640 in 9 years is $470

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

Let P represent the amount of money that Brooklyn should invest, hence:

Since the interest is 3.5% (0.035) in 9 years, therefore:

[tex]\sf 640=P\huge \text(1+\dfrac{0.035}{1}\huge \text)^{1\times9}[/tex]

[tex]\sf P=469.59[/tex]

The amount of money Brooklyn need to invest, for the value of the account to reach $640 in 9 years is $470

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The first four terms of the sequence defined by the formula an = -221 + 200n are: -21, 179, 379, and 579.

To find the first four terms of the sequence defined by the formula an = -221 + 200n, we can substitute the values of n from 1 to 4 into the formula and evaluate the expression.

When n = 1:

a1 = -221 + 200(1)

a1 = -221 + 200

a1 = -21

So, the first term of the sequence is -21.

When n = 2:

a2 = -221 + 200(2)

a2 = -221 + 400

a2 = 179

The second term of the sequence is 179.

When n = 3:

a3 = -221 + 200(3)

a3 = -221 + 600

a3 = 379

The third term of the sequence is 379.

When n = 4:

a4 = -221 + 200(4)

a4 = -221 + 800

a4 = 579

The fourth term of the sequence is 579.

Therefore, the first four terms of the sequence defined by the formula an = -221 + 200n are: -21, 179, 379, and 579.

Each term in the sequence is obtained by substituting the corresponding value of n into the formula and evaluating the expression. As n increases, the terms of the sequence increase by 200 each time.

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Brooklyn needs to invest $432.43, rounded to the nearest ten dollars.

To determine how much Brooklyn needs to invest in an account that pays a continuously compounded interest rate, we can use the formula:

A = [tex]Pe^(^r^t^)[/tex]

where A is the future value of the account, P is the principal investment, e is the mathematical constant approximately equal to 2.71828, r is the interest rate, and t is the time in years.

In this case, we want the future value of the account to be $640, the interest rate is 3.5% (or 0.035 as a decimal), and the time is 9 years. We can substitute these values into the formula and solve for P:

640 = [tex]Pe^(^0^.^0^3^5^*^9^)[/tex]

640 = Pe^0.315

P =[tex]640/e^0^.^3^1^5[/tex]

P = 432.43

Therefore, to have a future value of $640 in 9 years with a continuously compounded interest rate of 3.5%.

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The probability of each outcome would be 1/36.

Using 4 decimal places, the probability of each outcome in the equally likely outcome probability model would be 0.0278.

To calculate the probability of each outcome in the sample space when using the equally likely outcome probability model, we need to determine the total number of outcomes and then divide each outcome by the total.

Given that two dice are being rolled, there are 6 possible outcomes for each die, resulting in a total of 6 * 6 = 36 outcomes in the sample space.

To find the probability of each outcome, we divide 1 by the total number of outcomes (36).

Therefore, the probability of each outcome would be 1/36.

Using 4 decimal places, the probability of each outcome in the equally likely outcome probability model would be 0.0278.

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The total distance if he goes around the circle twice is 56.52 cm

The answer of this is equal to two times the circumference of the circle, remember that for a circle of radius R, the circumference is:

C = 2πR

with π = 3.14

Then in this case the length is:

L = 4πR

In this case the radius is 4.5cm, then the length is:

L = 4*3.14*4.5cm = 56.52 cm

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We have shown that AC:BC is indeed in the ratio 2:1 or 2:3. The ratio is 2:3 because AC is twice the length of AB, and BC is one-third the length of AB.

To show that AC:BC is in the ratio 2:3, we need to compare the lengths of AC and BC in terms of their respective expressions.

Given AB:AC = 1:2, we can represent the lengths of AB and AC as follows:

AB = 3x - 4

AC = 2(3x - 4) = 6x - 8

Next, we need to find the length of BC. Since AB and BC are segments of the same line, we can express BC in terms of AB and AC using the fact that the sum of two segments is equal to the length of the whole line. Therefore:

AB + BC = AC

Substituting the expressions we have for AB and AC:

(3x - 4) + BC = 6x - 8

Now, let's solve this equation for BC:

BC = 6x - 8 - (3x - 4)

BC = 6x - 8 - 3x + 4

BC = 3x - 4

We have found the length of BC, which is 3x - 4. Now we can compare the ratios of AC:BC:

AC:BC = (6x - 8):(3x - 4)

To simplify the ratio, we can factor out a common factor of 2:

AC:BC = 2(3x - 4):(3x - 4)

Notice that we have a common factor of (3x - 4) in the numerator and denominator. We can cancel out this common factor, resulting in:

AC:BC = 2:1

Therefore, we have shown that AC:BC is indeed in the ratio 2:1 or 2:3. The ratio is 2:3 because AC is twice the length of AB, and BC is one-third the length of AB.

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The calculated value of x is 3/2

The lengths of all three sides of the triangle are 11, 11 and 14

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

The triangle

The triangle is an isosceles triangle

So, we have

8x - 1 = 4x + 5

Evaluate

4x = 6

So, we have

x = 3/2

Recall that

x = 3/2

So, we have

4x + 5 = 4 * 3/2 + 5

4x + 5 = 11

Also, we have

2x + 11 = 2 * 3/2 + 11

2x + 11 = 14

Hence, the lengths of all three sides of the triangle are 11, 11 and 14

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Answer:

6√5 - 4√7

Step-by-step explanation:

To simplify the expression 3√5 - 2√7 + √45 - √28, we can simplify each radical term and then combine like terms.

First, let's simplify the radical terms:

√5 can't be simplified further because it is already in its simplest form.

√7 can't be simplified further.

√45 can be simplified as follows:

√45 = √(9 * 5) = √9 * √5 = 3√5

√28 can be simplified as follows:

√28 = √(4 * 7) = √4 * √7 = 2√7

Now let's substitute the simplified radical terms back into the original expression:

3√5 - 2√7 + √45 - √28 = 3√5 - 2√7 + 3√5 - 2√7

Next, we can combine like terms:

3√5 + 3√5 - 2√7 - 2√7 = 6√5 - 4√7

Therefore, the simplified form of the expression 3√5 - 2√7 + √45 - √28 is:

6√5 - 4√7

Hence, the correct answer is option c. 6√5 - 4√7.

Answer:

it's the second option

Step-by-step explanation:

as you can see , its a very hard question but dont ket that trick you !! first what you do is that you put the equation in groups

1.) 3/5 : 6.70

-2/7 = 1.41670131

+/45= 8.124905243

-/28= 2.833402621

thats the answer

now what we do is fine the same equation qith the exact answer

2/2 is 2.828427125

there you go !!

hope this helps people !!

Answer: 0.03125

Step-by-step explanation:

To find how much each of the students received, we must divide 1/8 by the amount of students (4). If it's asking for an answer in the form of a fraction you should try googling 0.03 as a fraction.

Answer:

The answer is,

[tex]p(x) = \sqrt[3]{2-x}[/tex]

Step-by-step explanation:

Jerrica would have to win 40 additional games in a row to have an 80% winning record. This would bring her total wins to 20 + 40 = 60, and her total games played to 35 + 40 = 75.

To determine how many games Jerrica would have to win in a row in order to have an 80% winning record, we need to calculate the number of games she needs to win out of a certain total.

Let's denote the number of games she needs to win in a row as x. If she wins x additional games, her total wins would be 20 + x, and her total games played would be 35 + x.

To have an 80% winning record, she would need to win 80% of the total games played. Mathematically, this can be expressed as:

(20 + x) / (35 + x) = 80 / 100

Cross-multiplying, we get:

100(20 + x) = 80(35 + x)

Expanding and simplifying:

2000 + 100x = 2800 + 80x

Subtracting 80x from both sides:

20x = 800

Dividing by 20:

x = 40

Jerrica would have to win 40 additional games in a row to have an 80% winning record. This would bring her total wins to 20 + 40 = 60, and her total games played to 35 + 40 = 75.

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Answer:

The given correlation is a strong positive correlation, and it is not likely causal.

We have given that,

The correlation coefficient relating the two variables is 0.74.

What is the correlation coefficient?

The correlation coefficient value is used to determine the strength of the linear relationship between two variables. The value ranges from - 1 to +1.

The correlation coefficient value is used to determine the strength of the linear relationship between two variables. The value ranges from - 1 to +1.

with negative values depicting a negative relationship and positive values showing a positive relationship.

The value of 0 implies that no relationship exists.

The closer the correlation coefficient value is to +1 or - 1, the greater the strength of the relationship between them.

Also, correlation does not mean causation.

Hence, a correlation coefficient of 0.74 depicts a strong positive relationship.

However, it doesn't imply causation.

We have the given correlation coefficient relating the two variables is 0.74 and it is near +1

Therefore, the given correlation is a strong positive correlation, and it is not likely causal.

Step-by-step explanation:

The method that determines the volume of the prism is simply multiply the area of the base by the height, and the result is 12.5 cm³. (option-a)

To determine the volume of the prism shown in the diagram, we need to multiply the area of the base by the height.

The base of the prism is a rectangle with dimensions 5 cm by 2 cm. Therefore, the area of the base is:

A = length x width = 5 cm x 2 cm = 10 cm²

The height of the prism is 2-¹ cm, which is equivalent to 5/4 cm.

Therefore, the volume of the prism is:

V = A x h = 10 cm² x 5/4 cm = 12.5 cm³

The expressions involving unit cubes and one-quarter cubes are not relevant to this problem and do not provide a method for finding the volume of the prism.

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The value of x is 3 / 2.

The side length of the triangle are 11, 11 and 14 units.

The triangle above is an isosceles triangle. Therefore, two sides of the triangles are equal and the base angles are equal.

Therefore, let's find the value of x in the triangle and the length of the three sides as follows;

Hence,

8x - 1 = 4x + 5

8x - 4x = 5 + 1

4x = 6

x = 6 / 4

x = 3 / 2

Therefore,

8x - 1 = 8(3 / 2) - 1 = 12 - 1 = 11 units

4x + 5 = 4(3 / 2) + 5 = 11 units

2x + 11 = 2(3 / 2) + 11 = 3 + 11 = 14 units

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The rational function for this problem is defined as follows:

y = (4x + 13)/(x + 3).

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.

The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.

The function has a vertical asymptote at x = -3, hence the denominator is given as follows:

x + 3.

The function has an horizontal asymptote at y = 4, with an intercept of 4.3, hence the numerator is given as follows:

4x + 13.

Thus the function is:

y = (4x + 13)/(x + 3).

The problem asks for the function rule.

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