1. There is a two digit number where the difference in the units digit and the tens digit is 5. If the digits are reversed, the
new number is the sum of twice the original number and seven. Find the number.

Answer:

£22

Step-by-step explanation:

x+1/2x=33

1.5x=33

33/1.5=22

The weekly allowance for Yasir last year is £22.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that Yasir received a 50% increase in his allowance this year. He now receives £33 a week.

The weekly allowance for last year will be calculated as,

1.5 x (X) = £33

X = £33 / 1.5

X = £330 / 15

X = £22

Therefore, Yasir's weekly allowance for last year is £22.

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m²+5mn+5n²

To factor the above, we need two factors of 5n², such the sum gives 5n and the product gives 5n²

No such factors exists, hence the polynomial is prime.

We have to identify the rational number.

Any number that can be expressed as a fraction is a rational number.

In this case the options are:

A. The square root of 3. This does not have a solution with finite number of decimals, so it can not be expressed as a fraction. Then, it is not rational.

B. The square root of 36, unlike the square root of 3, does have a rational solution: 6. So the square root of 36 is a rational number.

C. The square root of 7. This does not have a solution with finite number of decimals, so it can not be expressed as a fraction. Then, it is not rational.

D. The number π has an infinite number of decimals, so it can not be represented as a fraction. Thn, it is not a rational number.

nswer: O√36 [ption B]

The values of k for the different quadratic equation solutions are as follows

a  the equation 2x² - x + 3k = 0 has two distinct real roots

b. the equation 5x² - 2x + (2k − 1) = 0 has equal roots

ci the equation -x² + 3x + (k + 1) = 0 has real roots

d the equation 3kx² - 3x + 2 = 0 has no real solutions

Quadratic equations of the form ax² + bx + c = 0 is solved using the formula

[tex]-b+\frac{\sqrt{b^{2}-4ac } }{2a}[/tex]     OR     [tex]-b-\frac{\sqrt{b^{2}-4ac } }{2a}[/tex]

The equation b² - 4ac is called the discriminant and it is used as follows

To solve the equation and get two real roots: 2x² - x + 3k = 0

substituting the values gives

(-1)² - 4 * 2 * 3k > 0

1 - 24k > 0

1 > 24k

divide through by coefficient of k

k < 1/24

To solve the equation and get equal roots: 5x² - 2x + (2k − 1) = 0

substituting the values gives

(-2)² - 4 * 5 * (2k - 1) = 0

4 - 40k + 20 = 0

-40k = -24

divide through by coefficient of k

k = 3/5

To solve the equation and get real roots  -x² + 3x + (k + 1) = 0

substituting the values gives  

(3)² - 4 * -1 * (k+1) > 0

9 + 4k + 4> 0

4k > -13

divide through by coefficient of k

k > -3.25

To solve the equation and get  no real solutions  3kx² - 3x + 2 = 0

substituting the values gives  

(-3)² - 4 * 3k * 2 < 0

9 - 24k² > 0

9 > 24k²

divide through by coefficient of k²

k² < 24/9

k < ± 1.633

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Answer:

ax² + bx + c = 0 is solved using the formula

Step-by-step explanation:

Given:

The equation of the ellipse is,

Explanation:

The general equation of ellipse with center (h,k) is,

The center of te given ellipse is (2,-3).

Determine the value of a and b.

The value of a is more than b. so major axis is horiontal and minor axis is vertical.

The coordinates of endpoints of major axis are,

and

The coordinates of endpoints of minor axis,

and

or we can expressed coordinates of endpoints of minor axis as,

Answer:

Step-by-step explanation:Perpendicular lines have a slope that is the negative reciprocal of the given line.

For example, if a given line has the slope 3/2, the the perpendicular line would have the slope -2/3.

For the given line: y = 4x - 7, the perpendicular line would have a slope of -1/4

There isn't enough info in the question to determine the y-intercept. Literally, any y-intercept could work and the line would still be perpendicular. Is the line supposed to pass through a certain point?

Your answer would be something like: y = -1/4 x + b

b is the y-intercept...if your question paper is multiple choice, choose the answer with the slope of -1/4. If it's supposed to pass through a certain point (x,y) replace x and y with the values in that point and solve for b to get the y-intercept.

18480 feet are between her old and new house

Let's begin by listing out the information given to us:

From the question;

we are given the decimal numbers

If we consider dividing 0.04 by 0.004 we will have

Therefore, 0.04 is 10 times as much as 0.004

Also, if we consider dividing 0.004 by 0.04 we will get

Therefore, 0.004 is 1/10 the amount of 0.04

Hence

Given the decimals 0.04 and 0.004 we have

1. 0.04 is 10 times as much as 0.004

2. 0.004 is 1/10 the amount of 0.04

Answer: 4 tons

Step-by-step explanation:

Since the crew can clear 1/2 ton in 30 minutes, 4 hours has eight 30 minutes, which means that 8x1/2 = 4

Answer: 4 tons

Step-by-step explanation:

30 minutes multiplied by 2 is 1 hour and 1 half times 2 is 1 ton, so the crew can clear one ton every hour. 4 hours times 1 ton is 4 tons an hour.

hello

we're required to write an equation to represent the sequence

-2, 8, -32

first of all, let's identify the first term

first term = -2

common ratio = ?

c

The solution to the given inequality in interval notation is: -6 ≤ v ≤ 3

In this exercise, you're required to determine all the values of v that simultaneously satisfy given inequality. First of all, we would have to eliminate the fraction on the left-hand side of the inequality by adding using an appropriate lowest common denominator of 3 as follows:

(2 × |4v + 6|)/3 - 2/1 ≤ 10

[(2 × |4v + 6|) - (3)2]/3 ≤ 10

[(2 × |4v + 6|) - 6]/3 ≤ 10

Cross-multiplying, we have:

(2 × |4v + 6|) - 6 ≤ 10 × 3

(2 × |4v + 6|) - 6 ≤ 30

Adding 6 to both sides, we have:

(2 × |4v + 6|) - 6 + 6 ≤ 30 + 6

(2 × |4v + 6|) ≤ 36

Dividing both sides by 2, we have:

(2 × |4v + 6|)/2 ≤ 36/2

|4v + 6| ≤ 18

Evaluating the absolute value function, we have:

4v + 6 ≤ ±18

For the positive interval, we have:

4v ≤ 18 - 6

4v ≤ 12

v ≤ 12/4

v ≤ 3.

For the negative interval, we have:

4v ≥ -18 - 6

4v ≥ -24

v ≥ -24/4

v ≥ -6

Lastly, we would express the solution as an interval notation as follows:

-6 ≤ v ≤ 3

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there are infintely many solutions. The solution set is {(x, y)| x = 7y - 9} or {(x, y)| 2x - 14y = -18 (option B)

Given:

x = 7y - 9 . . .(1)

2x - 14y = -18 . . . (2)

To find:

the solution of the system of equations

To determine the value of x and y, we will apply the substitution method:

we will substitute for x in equation (2):

2(7y - 9) - 14y = -18

2(7y) + 2(-9) - 14y = -18

14y - 18 - 14y = -18

14y - 14y - 18 = -18

0 - 18 = -18

-18 = -18

The left-hand side of the equation is equal to the right side of the equation.

when this happens, it is called infinitely many solutions.

Hence, there are infintely many solutions. The solution set is {(x, y)| x = 7y - 9} or {(x, y)| 2x - 14y = -18 (option B)

Tracy's Termite Control has a net worth of $750,000.

The assets total $980,235.

Recall that the assets are the sum of liabilities and equity.

For the given case,

Assets = $980,235

Equity = $750,000

Let us substitute these values into the above formula and solve for liabilities

Therefore, the amount of the liabilities is $230,235

The 4th option is the correct answer.

We need to factor the following polynomial:

We can see that:

And

Then, we can use the following factor rule:

We have that:

Then, we can factor the polynomial as follows:

In summary, we have:

Answer:

distance = rate x time

Step-by-step explanation:

distance = ?

rate = 24 m/s

time = (35 x 60) = 2100 s

thus,

distance = 24 x 2100 = 50400 m

Answer

11 - 8 (5 -2) = -13

Explanation

11 - 8 (5 -2)

To solve this, we will first solve the one in the bracket

11 - 8 (5 -2)

= 11 - 8 (3)

= 11 - 24

= -13

Hope this Helps!!!

In order to evaluate this expression, let's calculate the operations in the left side and compare the final value with the value in the right side:

Since the values don't match, so the expression is FALSE.

The value of (x) will be equal to → x = 16 - K.

Perimeter is the measure of the length of the boundary of any two dimensional shape.

Given is a quadrilateral with its sides given.

The perimeter of this quadrilateral will be the sum of the length of its sides. Since, in the question, the final value of perimeter is not given, therefore we will assume it as K. The perimeter will be equal to -

(7x - 1) + (- 8x - 5x) + (6x + 13) + (4 - x) = K

7x - 1 - 8x - 5x + 6x + 13 + 4 - x = K

16 - x = K

x = 16 - K

Therefore, the value of (x) will be equal to → x = 16 - K.

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Answer:

oiutwecldvi ufa

Step-by-step explanation:

Answer:

$0.8625

Explanation:

The sales tax for the t-shirt will be 7.5% of the price. So, 7.5% of $11.50 can be calculated as:

So, the sales tax for this item is $0.8625

The value of f(2) would be 80 which is determined by substituting the value of x = 2in the given function ​f(x) = (x −2)(2x³ + 10x² + 16x + 34) + 80.

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

The given function below is:

​f(x) = 2x⁴ + 6x³ −4x² +2x + 12

​f(x) = (x −2)(2x³ + 10x² + 16x + 34) + 80

We have to determine the value of f(2).

⇒ ​f(x) = (x −2)(2x³ + 10x² + 16x + 34) + 80

Substitute the value of x = 2 in the given function,

⇒ ​f(x) = (2 −2)(2(2)³ + 10(2)² + 16(2) + 34) + 80

​⇒ f(x) = (0)(2(2)³ + 10(2)² + 16(2) + 34) + 80

​⇒ f(x) = 0 + 80

​⇒ f(x) = 80

Therefore, the value of f(2) would be 80.

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Answer: 5

Step-by-step explanation: add up the numbers to get 30 then divide by 6 (the amount of numbers) to get 5

Answer: 5

Step-by-step explanation:

the mean is the average. add the numbers together then divide by how many addends you have.

2 + 4 + 5 + 6 + 6 + 7 =  30

30/6 = 5

:)

Choice A

Is the answer

The value of probability P(A) is 0.60

The clear tree diagram is added as an attachment

The given parameters from the tree diagram are:

The probability is calculated using the following probability formula

P(A) = P(A and D) + P(A and C)

Substitute the known values in the above equation

P(A) = 0.6 * 0.7 + 0.6 * 0.3

Evaluate the products

P(A) = 0.42 + 0.18

Evaluate the sum

P(A) = 0.60

Hence, the value is 0.60

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ANSWER

A = 51°

EXPLANATION

ABC is a right triangle. We know the length of the hypotenuse, AB = 44 m, and the length of the adjacent leg to angle A, AC = 28 m. To find the measure of angle A we have to use the cosine of that angle,

Solving for A,

Replace with the known values and solve,

Hence, the measure of angle A is 51°, rounded to the nearest whole number.

From the basic knowledge of Trignometry,

We are meant to find sin S , sin R , cos S and cos R:

sin S = opposite / Hypoteuse = 18 / 26

sin R = opposite / Hypotenuse = 16 / 26

cos S = Adjacent / Hypotenuse = 16 / 26

cos R = Adjacent / Hypotenuse = 18 / 26

The area of the circular sector is given as:

Given that, radius= 60ft and angle =40 degrees

Answer:

=1/1024

Step-by-step explanation:

4^-5

=1/4^5

=1/1024

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