The sum of two numbers is 50 and twice the sum of the numbers is 100. Make a pair of equations and solve them to find the numbers. (3 mks)​

Amy's forth  account is the most over drawn of all the four accounts

What is the total balance of all accounts?

The total balance of all 4 accounts can be determined as the sum of all account balances, bearing in mind that a positive is added whereas an overdrawn balance is deducted

Total balance=$250-$45+$100+$x

The total balance=$130

the balance in the forth account=$x

Let us substitute $130 for the total balance

$130==$250-$45+$100+$x

$130=$305+$x

$x=$130-$305

$x=-$175

The fact that the forth account has  a balance of negative $175 means that it is also overdrawn, in essence, the correct option out of the 4 options is A, the forth account is most overdrawn because it is more overdrawn that the second account with a negative balance of $45.

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9514 1404 393

Answer:

  16

Step-by-step explanation:

The equation of a line with slope m=1 through the point (h, k) = (-5, 7) will be ...

  y -k = m(x -h)

  y -7 = x +5

  y = x +12

Then for x = 4, the value of y is ...

  y = 4 +12 = 16

The point is (4, x) = (4, 16), so x = 16.

Answer:

16

Step-by-step explanation:

Given that the slope of the line is 1 . And it passes through the points (-5,7) and (4,x) .We know that slope is difference of ordinate by difference of abssica . So that ,

\(\implies Slope =\dfrac{y_2-y_1}{x_2-x_1}\\\\\implies 1 =\dfrac{ 7-x}{-5-4} \\\\\implies 1 \times -9 = 7-x \\\\\implies -9 -7 = -x \\\\\implies \underline{\underline{ x = 16 }}\)

Hence the required answer is 16 .

Answer: Let X = the smaller of the two consecutive odd integers. Therefore (X + 2) = the larger of the two consecutive odd integers.

Refer to the attachment for calculation

\(\underline{\boxed{\bf \dfrac{dy}{dx}=\dfrac{-1}{\sqrt{-2x^3-7x^2+8x+28}}-\dfrac{cos^{-1}\dfrac{x}{2}}{\sqrt{(2x+7)^3}}}}\)

Answer:

\(\dfrac{dy}{dx}=-\dfrac{2x+7+\arccos\left(\dfrac{x}{2}\right)\sqrt{4-x^2}}{(2x+7)\sqrt{4-x^2}\sqrt{2x+7}}\)

Step-by-step explanation:

Quotient Rule

\(\textsf{If }\:\:y=\dfrac{u}{v} \:\textsf{ then}:\)

\(\implies \dfrac{dy}{dx}=\dfrac{v \dfrac{du}{dx}-u\dfrac{dv}{dx}}{v^2}\)

Given equation:

\(y=\dfrac{\arccos\left(\dfrac{x}{2}\right)}{\sqrt{2x+7}}\)

To differentiate the given equation, apply the Quotient Rule:

\(\textsf{Let }\:u=\arccos\left(\dfrac{x}{2}\right)\)

\(\textsf{If }y=\arccos x \implies \dfrac{dy}{dx}=-\dfrac{1}{\sqrt{1-x^2}}\)

\(\begin{aligned}\implies u=\arccos \left(\dfrac{x}{2}\right) \implies \dfrac{du}{dx}& =-\dfrac{1}{\sqrt{1- \left(\dfrac{x}{2}\right)^2}}\dfrac{d}{dx}\left(\dfrac{x}{2}\right)\\\\& =-\dfrac{1}{\sqrt{1- \left(\dfrac{x}{2}\right)^2}} \cdot \dfrac{1}{2}\\\\ & = -\dfrac{1}{2\sqrt{1- \left(\dfrac{x}{2}\right)^2}}\\\\& =-\dfrac{1}{2\sqrt{\dfrac{4-x^2}{4}}}\\\\& =-\dfrac{1}{\dfrac{2\sqrt{4-x^2}}{2}} \\\\ & = -\dfrac{1}{\sqrt{4-x^2}}\end{aligned}\)

\(\textsf{Let }\:v=\sqrt{2x+7}=(2x+7)^{\frac{1}{2}}\)

\(\begin{aligned}\implies \dfrac{dv}{dx} & =\dfrac{1}{2}(2x+7)^{-\frac{1}{2}} \cdot 2\\\\ & = (2x+7)^{-\frac{1}{2}}\\\\ & = \dfrac{1}{\sqrt{2x+7}}\end{aligned}\)

Therefore:

\(\implies \dfrac{dy}{dx}=\dfrac{-\dfrac{\sqrt{2x+7}}{\sqrt{4-x^2}}-\dfrac{\arccos\left(\dfrac{x}{2}\right)}{\sqrt{2x+7}}}{(\sqrt{2x+7})^2}\)

\(\implies \dfrac{dy}{dx}=\dfrac{-\dfrac{\sqrt{2x+7}}{\sqrt{4-x^2}}-\dfrac{\arccos\left(\dfrac{x}{2}\right)}{\sqrt{2x+7}}}{2x+7}\)

\(\implies \dfrac{dy}{dx}=\dfrac{-\dfrac{\sqrt{2x+7}\sqrt{2x+7}}{\sqrt{4-x^2}\sqrt{2x+7}}-\dfrac{\arccos\left(\dfrac{x}{2}\right)\sqrt{4-x^2}}{\sqrt{4-x^2}\sqrt{2x+7}}}{2x+7}\)

\(\implies \dfrac{dy}{dx}=\dfrac{-\dfrac{(2x+7)+\arccos\left(\dfrac{x}{2}\right)\sqrt{4-x^2}}{\sqrt{4-x^2}\sqrt{2x+7}}}{2x+7}\)

\(\implies \dfrac{dy}{dx}=-\dfrac{(2x+7)+\arccos\left(\dfrac{x}{2}\right)\sqrt{4-x^2}}{\sqrt{4-x^2}\sqrt{2x+7}}}\times\dfrac{1}{2x+7}\)

\(\implies \dfrac{dy}{dx}=-\dfrac{2x+7+\arccos\left(\dfrac{x}{2}\right)\sqrt{4-x^2}}{(2x+7)\sqrt{4-x^2}\sqrt{2x+7}}\)

Answer:

4:3

Step-by-step explanation:

He has 4 Soccer Medals, 3 Swimming Medals

So it would be 4:3

The solution is: the value of x is 13.5.

Here, we have,

We can use a ratio to solve

2        3

---- = ------

11        3+x

Using cross products

2(3+x) = 3*11

Distribute

6+2x = 33

Subtract 6

6+2x-6 = 33-6

2x = 27

Divide by 2

2x/2 = 27/2

x = 13.5

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complete question:

Solve for X

The amount that you will have in 3 years, given the interest rate and the amount won, is 1, 195, 618. 17 currency units

To find the amount earned in three years as a result of your lottery being invested, use the future value formula which is:

= Amount won x ( 1 + periodic  rate ) ^ number of periods

Periodic rate :

= 6 % / 4 quarters per year

= 1. 5 %

The number of periods is:

= 3 years x 4 quarters per year

= 12 quarters

The amount you will have in 3 years is:
= 1,000,000 x ( 1 + 1. 5 %) ¹²

= 1, 195, 618. 17 currency units

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Simplifying this equation, we get:

8 + 4k + 4k + 6 = 30

8k + 14 = 30

8k = 16

k = 2

Therefore, the value of k is 1.

In mathematics, a polynomial is an expression consisting of variables (usually represented by x), coefficients, and non-negative integer exponents, which are combined using the operations of addition, subtraction, and multiplication. For example,

\(3x^2 + 2x - 1\)

is a polynomial with three terms, or a "trinomial," where the variable x is raised to the powers of 2 and 1, and the coefficients are 3, 2, and -1.

The degree of a polynomial is the highest power of the variable in the expression. For example, the polynomial above has a degree of 2, since the highest power of x is 2.

Polynomials are used in many areas of mathematics, including algebra, calculus, and geometry, and are used to model many real-world phenomena.

We can use the remainder theorem, which states that if a polynomial f(x) is divided by (x - a), then the remainder is equal to f(a). In this case, we know that when the polynomial\(l x^3 + kx^2 + 2kx\) + 6 is divided by (x - 2), the remainder is 30. So, we can set up the following equation:

\(x^3 + kx^2 + 2kx + 6 = (x - 2)q(x) + 30\)

where q(x) is the quotient when. \(x^3 + kx^2 + 2kx + 6\) is divided by (x - 2). We don't need to know what q(x) is, since we're only interested in finding k.

Now, let's substitute x = 2 into the equation above:

\(2^3 + k(2^2) + 2k(2) + 6 = (2 - 2)q(2) + 30\)

Simplifying the left-hand side, we get:

\(8 + 4k + 4k + 6 = 30\)

\(16k = 16\)

\(k = 1\)

OR

8 + 4k + 4k + 6 = 30

8k + 14 = 30

8k = 16

k = 2

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(i) The first term (a) is 24 and the common difference (d) is -2.

(ii) The sum of the progression is 2520.

i) Finding the first term and common difference:

Given that the number of terms in the arithmetic progression is 40 and the last term is -54, we can use the formula for the nth term of an arithmetic progression to find the first term (a) and the common difference (d).

The nth term formula is: An = a + (n-1)d

Using the given information, we can substitute the values:

-54 = a + (40-1)d

-54 = a + 39d

We also know that the sum of the first 15 terms added to the sum of the first 30 terms is zero:

S15 + S30 = 0

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values for S15 and S30:

[(15/2)(2a + (15-1)d)] + [(30/2)(2a + (30-1)d)] = 0

Simplifying the equation:

15(2a + 14d) + 30(2a + 29d) = 0

30a + 210d + 60a + 870d = 0

90a + 1080d = 0

a + 12d = 0

a = -12d

Substituting this value into the equation -54 = a + 39d:

-54 = -12d + 39d

-54 = 27d

d = -2

Now we can find the value of a by substituting d = -2 into the equation a = -12d:

a = -12(-2)

a = 24

Therefore, the first term (a) is 24 and the common difference (d) is -2.

ii) Finding the sum of the progression:

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values:

S40 = (40/2)(2(24) + (40-1)(-2))

S40 = 20(48 - 39(-2))

S40 = 20(48 + 78)

S40 = 20(126)

S40 = 2520

Therefore, the sum of the arithmetic progression is 2520.

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Answer:

The answer is A.

Step-by-step explanation:

In a linear equation, y = mx + b, m is represented as gradient (slope) and b is the y-intercept.

So for this question, m is 2/3 and b is 1.

The entrance fee is d dollars, and the meal ticket is $4 less than the entrance fee -> Each meal ticket is d - 4

So, the total amount that the friends pay is 5(d-4)

Answer:

the correct answer is -1/16 i believe

In the given situation if the variance of the data values in a population is 441, the standard deviation of the data values is (B) 21.

The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean.

A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

The variance's square root is the standard deviation of the data values:

S = √V = √441 = 21

Therefore, in the given situation if the variance of the data values in a population is 441, the standard deviation of the data values is (B) 21.

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The value of the expression 4c² -9(c-1)/5c when c= 6 is 142.5

The value of an expression is the value which one gets after putting the value of the variables in the expression.

let 4x+ 2 be an expression and we want to know its value on x= 1 , then the value is 4(1)+2 = 6

Given an expression 4c² -9(c-1)/5c , then its value at c= 6 :

4(6)² -9(6-1)/5(6) =144 - 9(5)/5(6) = 144-3/2 = 285/2 = 142.5

The value of 4c² -9(c-1)/5c at c= 6 is 142.5

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Answer:

There is an infinite number of possibilities because you gave us no answer choices. Here are some of them:

2/128

4/256

6/384

8/512

And we could go on and on with this.

Hope this helps! If it did, please give brainliest! It would help a lot! Thanks! :D

Answer:  It was the crossroads for four major railroads. President Abraham Lincoln knew that if his army could capture Chattanooga, vital Confederate supply lines would be severed, and the war would be closer to an end.

Step-by-step explanation:

To complete the sequence "7444> →→19-", we need to find the missing terms that fit the pattern established by the given numbers. Let's analyze the sequence and identify any discernible pattern or rule.

Looking at the sequence, we can observe that each number is decreasing by a certain value. In this case, the first number is 7444, and the second number is 19, indicating a decrease of 7425. Now, we need to continue this pattern.

To find the third missing term, we subtract 7425 from 19, resulting in -7406. Therefore, the third missing term is -7406

To find the fourth missing term, we subtract 7425 from -7406, resulting in -14831. Therefore, the fourth missing term is -14831.

To find the fifth missing term, we subtract 7425 from -14831, resulting in -22256. Therefore, the fifth missing term is -22256.

Therefore, the completed sequence is:

7444> →→19- → -7406 → -14831 → -22256

Each term in the sequence is obtained by subtracting 7425 from the previous term.

It's important to note that this solution assumes a linear pattern in which the same subtraction value is applied to each term. However, without additional context or information about the sequence, there could be alternative patterns or interpretations.

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Answer:

21 ft. long

Step-by-step explanation:

28/x = 8/6

Cross Multiply:

8x=168

Divide Both Sides:

8x÷8=x

168÷8=21

So...

x=21

The palm tree is 21 feet long :)

Answer:

1/4

Step-by-step explanation:

Completing the square

x^2 -x

Take the coefficient of the x term

-1

Divide by 2

-1/2

Square it

(-1/2) ^2 = 1/4

Add this to each side

Given:

Triangle ABC is an isosceles triangle. Angles B and C are base angles, with measurements of

Required:

To find the angle A.

Explanation:

Triangle ABC is an isosceles triangle.

Therefore,

Now,

The angle A is,

Final Answer:

Answer: No

Step-by-step explanation:

to be proportional, both numbers have to increase by the same number

because if u multiply 6 by 2 you get 12, but when you multiply 10 by 2 you get 20, not 60 it would be proportional if you said 6 and 10 in to 12 and 20 in

Answer:

The slope of y=-3x+2 is B. -3

X = 31, Y = 63 satisfy the case of 0 ≤ Y < 100 as an expression.

An algebraic expression in mathematics is an expression that consists of variables and constants and algebraic operations (addition, subtraction, etc.). Expressions are made up of concepts.

Assume Kaimi was supposed to be paid X dollars Y cents (0 ≤ Y ≤ 100)

But the teller gave him Y dollars X cents.

Thus kaimi has 100Y + X cents.

A nickel is worth 5 cents.

Hence, after buying the piece of candy for a nickel, Kaimi would be left with 100Y + X - 5 cents.

This is twice his paycheck:

⇒ 100Y + X - 5 = 2(100X + Y)

⇒ 100Y + X - 5 = 200X + 2Y

⇒ 98Y - 199X = 5

199 = 98 × 2 + 3 ⇒ 3 = 199 - 98 × 2

98 = 3 × 32 + 2 ⇒ 2 = 98 - 3 × 32

3 = 2 × 1 + 1 ⇒ 1 = 3 - 2 × 1

2 = 1 × 2 + 0 ⇒ ged(199, 98) = 1

1 = 3 - 2 × 1

= 3 - (98 - 3 × 32) × 1                [∵ 2 = 98 - 3 × 32]

= 3 - 98 × 1 + 3 × 32

= 3 × 33 - 98 × 1

= (199 - 98 × 2) × 33 - 98 × 1    [∵ 3 = 199 - 98 × 2]

= 199 × 33 - 98 × 67

⇒ 1 = 199 × 33 - 98 × 67

⇒ 5(1) = 5 (199 × 33 - 98 × 67)

⇒ 5 = 199(165) - 98(335)         [∵ 5 ×33 = 165, 5 × 67 = 335]

⇒ 199(165) - 98(335) = 5

⇒ 98(-335) - 199(-165) = 5

Hence, (X,Y) = (-165, -335) is a solution to 98Y - 199X = 5

But it is required that 0 ≤ Y < 100

Now since it is the difference of two quantities, 98Y and 199X, that is a constant, 5, either both of these quantities will increase simultaneously or both will decrease simultaneously.

Hence, either both X, Y will increase or both, X, Y will decrease.

To bring Y = -335 in the range of 0 ≤ Y < 100, it needs to be increased.

Hence, both X, Y will increase.

X will increase by the absolute value of the coefficient of Y and vice-versa. Hence, X will increase by 98 and Y will increased by 199 to give

(X, Y) = (-165 + 98, -335 +199) = (-67, -136)

Still, it is not the case that 0 ≤ Y < 100

Hence, again X will increase by 98 and Y will increase by 199 to give

(X, Y) = (-67 +98, -136 +199) = (31, 63)

Now, it is the case that 0 ≤ Y = 63 < 100

∴ X = 31, Y = 63

Note that the increasing X again by 98 and Y by 199 will violate

0 ≤ Y < 100. Hence, this is the unique solution.

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Answer:

16 is natural, whole, and an integer. Since it can also be written as the ratio 16:1 or the fraction 16/1

Step-by-step explanation:

I need to deposit $1558.41 to have $2000 in the account in 5 years.

What is compound interest?

The interest charged on a debt or deposit is known as compound interest. It is the idea that we use the most regularly. Compound interest is calculated for a sum based on both the principal and cumulative interest.

    ∴ Compound interest = P(1 + \(\frac{r}{100*12}\))ⁿ  (∵ for monthly interest)

        P = Principal

        r = rate of interest per month

        n = number of months

Given:

r = 5% per month

n = 5 years = 5*12 = 60 months

  CI = P (1+5/(12 * 100))⁶⁰

2000 = P(1.0041)⁶⁰

2000 = P(1.2834)

      P = 1558.41

Therefore, the amount required to deposit is 1558.41 dollars to get 2000 dollars after 5 years with 5 percent interest per month.

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The fare for a 500-mile trip is 164.

The equation provided in the question is known as a linear equation. A linear equation is an equation that has a single variable that is raised to the power of one.

The general form of a linear equation is:

y = mx + b

Where:

In the equation used to calculate the fare, y=0.28x+24, 0.28 is the variable cost and 24 is the fixed cost.

Cost of a 500-mile trip = y=0.28(500) +24

y = 140 + 24

y = 164

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Answer:

The answer is 64.29% hope it helps

Answer:

35.71 percent

Step-by-step explanation:

Percentage change= \(\frac{Old value-New value}{Old value}\)x100

= \(\frac{70-45}{70}\)x100

= \(\frac{25}{70}\)x100 = 35.71 percent (rounded to 2 decimal places)

Answer:

I’m sorry but I don’t understand the question

Step-by-step explanation: