Which fraction is less than 1/2?

A. 3/8

B. 5/8

C. 5/7

D. 9/16

Answer:

10 hours

Step-by-step explanation:

380 - 80 = 300

30 : 1 = 300 : x

x = 300 / 30

x = 10

Answer:

11.25

Step-by-step explanation:

By substitution; x = 4 and y = -31

An equation is a mathematical statement that shows that two mathematical expressions are equal. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. Equations can be solved to find the value of an unknown variable representing an unknown quantity.

y=-6x-7 --- 1

7x+y=-3 --- 2

Substituting y as 6x - 7 in equation 2

7x + (-6x - 7) = -3

7x - 6x - 7 = -3

x - 7 = -3

x = -3 + 7

x = 4

Substitute x as 4 in equation 1

y = -6x - 7

y = -6(4) - 7

y = -24 - 7

y = -31

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The correct option for the given sum is option B. The point (2,-9) paired with (2, 3), will make a side equal to this length.

Let the other point of the pentagon will be M(n, o).

The given point be A (a, b)

Also given one of the sides of a pentagon has length 12.

Now, we need to find the distance between the two points,

Distance between two points: |AM| = √\((a-n)^2+(b-o)^2\)

Now,

\(12 = \sqrt{(2-n)^2+(3-o)^2}\)

\((12)^2\) = \((2-n)^2+(3-o)^2\)

\((2-n)^2+(3-o)^2\) = 144 ----------------------------- eq (1)

Now, check every point for the values to match with equation (1)

Option A: \((2-14)^2+(3-15)^2\) = 288. So the option is false.

Option B:

\((2-2)^2+(3-(-9))^2\) =114

0+114 =114

Therefore option B is correct. The other point is (2,-9).

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Answer:

4. ASA theorem

Step-by-step explanation:

The values of f(x) for the given x - values rounded to 4 decimal places are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013 respectively

Given the function :

Substitute the given value of x to obtain the corresponding f(x) values :

x = -0.6

f(x) = (tanπ(-0.6))/7(-0.6) = 0.0078358

x = -0.51

f(x) = (tanπ(-0.51))/7(-0.51) = 0.0078350

x = -0.501

f(x) = (tanπ(-0.501))/7(-0.501) = 0.001967

x = -0.5

f(x) = (tanπ(-0.5))/7(-0.5) = 0.001959

x = -0.4999

f(x) = (tanπ(-0.4999))/7(-0.4999) = 0.001958

x = 0.499

f(x) = (tanπ(-0.499))/7(-0.499) = 0.001951

x = -0.49

f(x) = (tanπ(-0.49))/7(-0.49) = 0.00188

x = -0.4

f(x) = (tanπ(-0.4))/7(-0.4) = 0.00125

Therefore, values which complete the table are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013

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Answer:

69420

Step-by-step explanation:

when the ball goes whooo, it's max height goes sicko mode.

equation: β⇵πΔ = 69 times

∨xe⇵Δ 420

answer:

69420

Answer:

100

Step-by-step explanation:

x+80=180 because straight angle is 180 degrees.

x=100

Answer:

100 degrees

Step-by-step explanation:

when you're trying to solve a problem like this, just subtract the number you have from 180.

Using percentage, the true proportion of registered voters who are Democrats is = 64.

What do you mean by percentage?

A percentage's denominator, often referred to as a ratio's or a fraction's, is always 100. Sam, for instance, would have gotten 30 out of a potential 100 points if his math test score had been 30%.

It is written as 30:100 in ratio form and 30/100 in fraction form. In this context, "%" is read as "percent" or "percentage" to represent a percentage.

In the question,

Sample size, n = 140.

Now 46% of the registered voters are Democrats.

Now the no. of registered voters =

46% of 140

= 46/100 × 140

= 6440/100

= 64.4

≈ 64

Therefore, 64 is the true proportion of registered voters who are Democrats.

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The first equation is incorrect.

The second equation is correct.

The third equation is correct.

Let's go through each equation and determine whether it is correct or incorrect:

(b²+7b-9)+(4b-6b²) = -8b² + 14b-9

To determine if this equation is correct, we need to simplify both sides and check if they are equal.

On the left side:

(b²+7b-9)+(4b-6b²) = b² - 6b² + 7b + 4b - 9 = -5b² + 11b - 9

On the right side:

-8b² + 14b - 9

Comparing both sides, we can see that -5b² + 11b - 9 is not equal to -8b² + 14b - 9. Therefore, the equation is incorrect.

(4a+6)-(3a²-9a+1)=-3a²+ 13a +5

Again, we need to simplify both sides of the equation and check if they are equal.

On the left side:

(4a+6)-(3a²-9a+1) = 4a + 6 - 3a² + 9a - 1 = -3a² + 13a + 5

On the right side:

-3a² + 13a + 5

Comparing both sides, we can see that -3a² + 13a + 5 is equal to -3a² + 13a + 5. Therefore, the equation is correct.

(12c-8c²)+(5c²- 10c) = -3c²+2c

Again, let's simplify both sides and compare them.

On the left side:

(12c-8c²)+(5c²- 10c) = 12c - 8c² + 5c² - 10c = -3c² + 2c

On the right side:

-3c² + 2c

Comparing both sides, we can see that -3c² + 2c is equal to -3c² + 2c. Therefore, the equation is correct.

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The value of X is 7.

Given that the set of number are in pattern,
X, 5, 9, 27, 15, 21.

To find the value of X such that given numbers are in pattern.

The next three number are three times of first three numbers respectively.

Let a, b, c is the first three numbers then 3a, 3b, 3c are next three numbers.

Consider the given set of numbers,  X, 5, 9, 9 × 3, 5 × 3, 21.

By using the data and the pattern set gives,

3X = 21.

Divide by 7 on both sides,

X = 7.

Hence, the value of X is 3

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Answer:

it's 4

Step-by-step explanation:

y - y1= m(x- x1)

y- (-1)= 2(x - 3)

y+ 1= 2x- 6

y= 2x - 7

Answer:

4x² + 22x - 12

Step-by-step explanation:

A = bh/2

A = (4x - 2)(2x + 12)/2

A = (8x² + 48x - 4x - 24)/2

A = (8x² + 44x - 24)/2

A = 4x² + 22x - 12

The graph of the function y = 5|x - 4| is added as an attachment

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

y = 5|x - 4|

The above function is an absolute value function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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Answer:

Starting with the equation:

(x + 1)^2 = 13/4

We can use the square root property, which states that if a^2 = b, then a is equal to the positive or negative square root of b.

Taking the square root of both sides, we get:

x + 1 = ±√(13/4)

Simplifying under the radical:

x + 1 = ±(√13)/2

Now we can solve for x by subtracting 1 from both sides:

x = -1 ± (√13)/2

Therefore, the solutions to the equation are:

x = -1 + (√13)/2 or x = -1 - (√13)/2

Step-by-step explanation:

Amount to be repaid for Bank A is $2,696.625 and Amount to be repaid for Bank B is $2,741.25. However, I will choose Bank B because it offers a lower interest rate.

The formula to calculate the simple interest is;

I = PRT

Where;

P is principal

R is rate

T is time

Now, we are given that;

Bank A;

Principal amount; P = $2550

Interest rate; R = 11.5% = 0.115

Time; t = 6 months = 0.5 years

Thus;

I = (2550 * 0.115 * 0.5)

I = $146.625

Amount to be repaid = 2550 + 146.625

Amount to be repaid = $2,696.625

Bank B;

Principal amount; P = $2550

Interest rate; R = 7.5% = 0.075

Time; t = 12 months = 1 year

Thus;

I = (2550 * 0.075 * 1)

I = $191.25

Amount to be repaid = 2550 + 191.25 = $2,741.25

Thus, bank B offers a more favorable interest rate and as such would be the preferred bank.

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Answer:

\(4*6^\frac{5}{2}\)

Step-by-step explanation:

Use \(\sqrt[n]{a^x}=a^{\frac{x}{n} }\) to rewrite \(\sqrt{6^5}\) as \(6^\frac{5}{2}\).

\(4*6^\frac{5}{2}\)

Answer:

Step-by-step explanation:

Comment

The formula that relates edges faces and vertices is  F + V = E + 2

Givens

Edges (E): 37

Faces (F) = 25

Vertices: x

Solution

25 + x = 37 + 2                Subtract 25 from both sides.

25-25 +x= 37 - 25 + 2    Combine

x = 12 + 2

x = 14

Answer: The vertices = 14

The net which represents the pyramid is: B. A square with a triangle connected to each side with a dotted line.

A square pyramid can be defined as a type of pyramid that has a square base, four (4) triangular sides, five (5) vertices, and eight (8) edges.

In this context, we can logically deduce that the net which represents the pyramid is a square with a triangle that is connected to each side with a dotted line as illustrated in the image attached below.

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Complete Question:

Which net represents the pyramid below? There are four squares attached left to right and a square above and below the last square. There are three rectangles connected vertically with dotted lines. There are triangles connected to the middle rectangle.

A. A hexagon with a triangle connected with a dotted line to each of the sides.

B. A square with a triangle connected to each side with a dotted line.

The percentage that can be filled with $3 in 1990 is: 29.41%

To calculate percentage growth rate:

Beginning:

Calculate the difference (increase) between the two numbers you are comparing. after that:

Divide the increment by the original number and multiply the result by 100. Growth rate = increment / original number * 100.  

We are told that it cost $3 to fill a gas tank as at 1970.

Now, there was a percentage price increase of (78.8 - 23.1)% = 55.2% from 1970 to 1990. Thus:

Cost of a gallon in 1970 = $0.36

Thus, number of gallons bought with $3 = 3/0.36 = 8.33 gallons at full tank

Now, in 1990, the cost is $1.23 and as such:

Quantity that can be bought = 3/1.23 = 2.45 gallons

Percentage of tank filled = 2.45/8.33 * 100% = 29.41%

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Answer:

-4 is the answer

Step-by-step explanation:

Answer:

19 - 42x

Step-by-step explanation:

To differentiate this, we must use the product rule
f'(x) = (7x+3)'(4-3x) + (4-3x)'(7x+3)
= (7)(4-3x) + (-3)(7x+3)
= 28 - 21x - 21x - 9
= 19 - 42x

Answer:

71/12 = 5 11/12

Step-by-step explanation:

To solve this equation you first have to put the whole number with fraction (mixed number) and convert it into an improper fraction. To do this you have to multiply the whole number by the denominator which is 6 x 2 and you'd get 12 but then you still have the numerator so then you add your answer with the numerator and you'd get 12+1 which is 13. So your improper fraction is 13/2.

Now you set up your equation and you'd subtract. But your denominators are not the same so you have to figure out and find the common denominator. Which is 12. So then for 13/2 you'd multiply both of them by 6 and you'd get 78/12. And the 2nd one you'd multiply it by 1 getting 7/12.

Once you get to this point now you can properly set up the equation and subtract. You'd subtract 78/12 - 7/12 getting 71/12 or if you want it as a mixed number (whole number with fraction) then it is 5 11/12.

(I tried to explain how I got the answer...hopefully you were able to understand how I did it...)

The denominator is zero (0/0 is undefined), we cannot determine the exact value of f(-3) using this equation.

To solve the given equations, we need to find the value of the function f(x) for specific values of x.

"If f(x) / (x - 2) = x³ + 2x - 4 + 13/(x - 2), what is f(2)?"

To find f(2), we can substitute x = 2 into the equation and solve for f(2).

Plugging in x = 2, we get:

f(2) / (2 - 2) = 2³ + 2(2) - 4 + 13/(2 - 2)

Since the denominator is zero (2 - 2 = 0), the equation is undefined. Therefore, there is no solution for f(2) in this case.

"If f(x) / (x + 3) = 3x² - 4x + 2, what is f(-3)?"

To find f(-3), we can substitute x = -3 into the equation and solve for f(-3).

Plugging in x = -3, we get:

f(-3) / (-3 + 3) = 3(-3)² - 4(-3) + 2

Simplifying, we have:

f(-3) / 0 = 3(9) + 12 + 2

f(-3) / 0 = 27 + 12 + 2

f(-3) / 0 = 41

Additional information or context is needed to solve for f(-3).

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if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

Calculating the loan amount for each brand by subtracting the down payment from the cash price:

Loan amount for Daewoo = RM1,899 - RM300 = RM1,599

Loan amount for Daikin = RM1,699 - RM300 = RM1,399

Loan amount for Mitsubishi = RM1,999 - RM300 = RM1,699

Calculating the interest charge for each brand:

Interest charge for Daewoo = Loan amount for Daewoo * Interest rate = RM1,599 * 0.04 = RM63.96

Interest charge for Daikin = Loan amount for Daikin * Interest rate = RM1,399 * 0.04 = RM55.96

Interest charge for Mitsubishi = Loan amount for Mitsubishi * Interest rate = RM1,699 * 0.04 = RM67.96

To find the monthly installment price, divide the total amount (cash price + interest charge) by the number of monthly installments:

Monthly installment price for Daewoo = (Cash price of Daewoo + Interest charge for Daewoo) / Number of monthly installments = (RM1,899 + RM63.96) / 18 ≈ RM107.22

Monthly installment price for Daikin = (Cash price of Daikin + Interest charge for Daikin) / Number of monthly installments = (RM1,699 + RM55.96) / 18 ≈ RM98.89

Monthly installment price for Mitsubishi = (Cash price of Mitsubishi + Interest charge for Mitsubishi) / Number of monthly installments = (RM1,999 + RM67.96) / 18 ≈ RM116.72

Therefore, if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

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The Pythagorean theorem is the idea that the sum of the two legs which are both squared is equal to the hypotenuse's length squared.

     *look at the image I attached for a better explanation

By looking at the picture, we are missing the leg's length, and by using the Pythagorean theorem, we get the equation

    \(?^2+5^2 = 13^2\\?^2 + 25 = 169\\?^2 = 144\\? = 12\)

Thus the missing side length is 12 cm

Hope that helps!

The domain and the range of the function are given as follows:

The function approaches y = 0 as x approaches positive infinity.

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