please help me, I don't understand this question.

Michael has recently opened a savings account. The banker gave him an equation to predict his balance at any given month, assuming he made no further deposits nor withdrawals. The equation is as follows: b=975(1.003)^m


where "b" is the balance of the account, and "m" represents the number of months the account has been open.

a) How much did Michael deposit when he first opened the account?

b) Is this a case of exponential growth or exponential decay? How do you know?

c) What is the monthly interest rate on the account?

d) What is the account balance after 6 months?

...after 12 months?

e) How many months will it take to have at least $1000 in the account?


Thank you in advance!

In the quadrilateral ACDE, we can identify two congruent angles: angle CDA and angle C'EA.

In the given diagram, we have ACDE as a quadrilateral, and we know that CD is congruent to CE. To identify two congruent angles, let's examine the properties of the quadrilateral.

Since ACDE is not specified to be a particular type of quadrilateral (such as a parallelogram or rectangle), we cannot directly infer congruent angles from its properties.

However, we can make use of some general properties of quadrilaterals to identify two congruent angles. One property is that the sum of the interior angles of a quadrilateral is always 360 degrees.

Let's consider angle C as one of the angles in ACDE. Since CD is congruent to CE, we can denote angle CDE as angle C' to represent the congruent angles.

Now, using the property that the sum of the interior angles of a quadrilateral is 360 degrees, we can express the relationship between the angles of ACDE as:

∠ACD + ∠CDE + ∠DEA + ∠EAC = 360 degrees

Since CD is congruent to CE, angles CDA and CEA are also congruent (opposite angles in a quadrilateral). So, we can rewrite the equation as:

∠ACD + ∠CDA + ∠C'EA + ∠EAC = 360 degrees

Since we want to identify two congruent angles, let's focus on angles CDA and C'EA. These two angles are formed by the intersection of the congruent sides CD and CE with different adjacent sides.

Therefore, we can conclude that angles CDA and C'EA are congruent in ACDE.

In summary, in the quadrilateral ACDE, we can identify two congruent angles: angle CDA and angle C'EA.

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The coordinates of point P are (5, -3.5). The equation of the circle is \((x - 5)^2 + (y + 3.5)^2 = 1.5^2\). The equation of KL is y = (-4/3)x + 22/3.

To find the coordinates of point P, we can first find the midpoint of MN, which is the center of the circle. The midpoint formula is given by:

Midpoint = ( (x1 + x2) / 2 , (y1 + y2) / 2 )

Using the coordinates of M(3,-5) and N(7,-2), we can calculate the midpoint:

Midpoint = ( (3 + 7) / 2 , (-5 + -2) / 2 ) = (5, -3.5)

Since the midpoint of MN is the center of the circle, the coordinates of P will be the same as the coordinates of the center, which are (5, -3.5).

i. To determine the equation of the circle in the form of \((x-a)^2\) + \((y-b)^2\) = \(r^2\), we can use the center and any point on the circle. We can use point N(7,-2), which lies on the circle.

The radius of the circle is half the length of PN. Therefore, the radius is given by:

Radius =\(1/2 * \sqrt((7 - 5)^2 + (-2 - (-3.5))^2) = 1.5\)

Substituting the values into the equation, we get:

\((x - 5)^2 + (y + 3.5)^2 = 1.5^2\)

ii. To determine the equation of KL in the form of y = mx + c, we can use the slope of the tangent line.

The slope of KL can be calculated as the negative reciprocal of the slope of the radius line MN. The slope of MN is given by:

m = (y2 - y1) / (x2 - x1) = (-2 - (-3.5)) / (7 - 5) = 1.5 / 2 = 0.75

The negative reciprocal of 0.75 is -4/3, which represents the slope of KL.

Using the point N(7,-2) and the slope -4/3, we can use the point-slope form of a line to find the equation of KL:

y - (-2) = (-4/3)(x - 7)

y + 2 = (-4/3)x + 28/3

y = (-4/3)x + 22/3

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To find the polar equation of a conic with focus at the pole, directrix y=3, and eccentricity of 2, we can use the definition of a conic in polar coordinates.

The general form of the polar equation for a conic with focus at the pole is given by:

r = \(\frac{ed}{1+e\cos(\theta-\theta_0)}\)

Where:

- r is the distance from the origin (pole) to a point on the conic.

- e is the eccentricity.

- d is the distance from the pole to the directrix.

- θ is the angle between the polar axis and the line connecting the pole to a point on the conic.

- θ_0 is the angle between the polar axis and the line connecting the pole to the focus.

In this case, the focus is at the pole, so θ_0 = 0. The directrix is y = 3, which means its distance from the pole is d = 3. The eccentricity is given as 2, so e = 2.

Substituting these values into the general equation, we get:

r =\(\frac{2\cdot3}{1+2\cos(\theta-0)}\)

Simplifying further:

r =\(\frac{6}{1+2\cos(\theta)}\)

Therefore, the polar equation of the conic with focus at the pole, directrix y=3, and eccentricity of 2 is:

r =\(\frac{6}{1+2\cos(\theta)}.\)

This equation describes the shape of the conic in polar coordinates, where r represents the distance from the origin to a point on the conic, and θ represents the angle between the polar axis and the line connecting the origin to the point.

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Answer:

Its the second one....

Step-by-step explanation:

Answer:

11x+12

Step-by-step explanation:

3x + 2x+2 + x+10 + 5x= 11x+12

Answer:

top

question 1 is 25

question 2 is 0.2

------------------------------

bottom

question 3 is the second graph

the last question is the first graph

Step-by-step explanation:

Answer:

1350.ans

Step-by-step explanation:

please give me marks

The Software E costs in the long term is $10,500

Cost sharing is a term used to describe a situation in which two or more parties agree to share the cost of a particular expense or project. In other words, it refers to a joint financial contribution made by multiple parties towards a common goal.

Software E purchased in $6,000. If person will be satisfied then he will purchase it for long term, so the satisfaction rate is 75% of original cost.

Then, the Software E costs in the long term = $6,000 + ($6,000× 75%)

\(=6,000 + (6,000 * \frac{75}{100} )\)

\(=6,000 + (60 * 75 )\)

\(=6,000 + 4500\\= 10,500\)

Therefore, the Software E costs in the long term is $10,500

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Answer:

22 gallons

Step-by-step explanation:

280 miles / 56 gallons = 5 miles per gallon

110 miles/5 mpg = 22 gallons

Answer:

Thanks

Step-by-step explanation:

Thanks

Answer:

C

Step-by-step explanation:

divide 14 by 4 to solve it, you get 3.5 or 3 1/2

The height of the tree after 6 years can be expressed as "3 feet + 6f feet."

The correct answer is A. 3f + 6 feet.

To determine the current height of the tree in terms of "f,"

let's analyze the given information.

We know that the tree was initially 3 feet tall when it was planted 6 years ago.

Since the tree grows every year, we can assume that its growth rate is consistent.

Let's denote the current height of the tree as "h" (in feet).

After 6 years, the tree has grown by a certain amount, which we'll represent as "6f" (6 years multiplied by the growth rate "f").

Therefore, the height of the tree after 6 years can be expressed as "3 feet + 6f feet."

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Given:

The functions are

\(f(x)=4x^2+7x-5\)

\(g(x)=-9x^2+4x-13\)

To find:

The functions \((f+g)(x)\) and \((f-g)(x)\).

Solution:

We know that,

\((f+g)(x)=f(x)+g(x)\)

\((f+g)(x)=4x^2+7x-5-9x^2+4x-13\)

\((f+g)(x)=(4x^2-9x^2)+(7x+4x)+(-5-13)\)

\((f+g)(x)=-5x^2+11x-18\)

And,

\((f-g)(x)=f(x)-g(x)\)

\((f-g)(x)=(4x^2+7x-5)-(-9x^2+4x-13)\)

\((f+g)(x)=4x^2+7x-5+9x^2-4x+13\)

\((f+g)(x)=(4x^2+9x^2)+(7x-4x)+(-5+13)\)

\((f-g)(x)=13x^2+3x+8\)

Therefore, the required functions are \((f+g)(x)=-5x^2+11x-18\)

and \((f-g)(x)=13x^2+3x+8\).

Answer:

D

Step-by-step explanation:

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Vertex: (−3,0)(-3,0)

Focus: (−3,14)(-3,14)

Axis of Symmetry: x=−3

Hope it helped :)

Answer:

Step-by-step explanation:

Hey, again!

So, first, get the 43 isolated. So, add -9p on both sides.

This will give you 4p+11>43

Next, subtract 11 on both sides.

You will get 4p>32

Next, divide 4 on both sides

This  will give you p>8.

Hope this helps!!!

The solution of the equation for t is t = i/pr

The equation is given as

i = prt

Divide both sides of the equation by p

So, we have the following equation

i/p = prt/p

Divide both sides of the equation by r

So, we have the following equation

i/pr = prt/pr

Evaluate the quotients

i/pr = t

Rewrite as

t = i/pr

By the above computation, we changed the subject of the formula in i = prt from i to t.

This implies that solving for t is a concept of subject of formula

Hence, the solution is t = i/pr

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Given statement solution is :- The present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

To calculate the present value of an investment with compound interest, we can use the formula for the present value of an annuity:

PV = A *\((1 - (1 + r)^(-n)) / r\)

Where:

PV = Present value

A = Annual payment or cash flow

r = Interest rate per period

n = Number of periods

In this case, the annual payment (A) is R13,000, the interest rate (r) is 10% per year, and the investment is made for 8 years (n).

Using the formula and substituting the given values, we can calculate the present value:

PV = \(13000 * (1 - (1 + 0.10)^(-8)) / 0.10\)

Calculating this expression:

PV = \(13000 * (1 - 1.10^(-8)) / 0.10\)

= 13000 * (1 - 0.46318) / 0.10

= 13000 * 0.53682 / 0.10

= 6977.66 / 0.10

= 69776.6

Therefore, the present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

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Here, we want to get the common factor when the two given expressions are factorised

We can factorize the first expression by the use of differeence of two squares

We have this as;

For the second expression, we have the factorization as follows;

What this mean is that we have the common factor of the two expressions as (x-3)

Answer:

Step-by-step explanation: I always like to make sure I am clear about the question. It seems like the question is:

you have 3 variables; H, N, and S. Using ( ) to represent multiplication

If

(H)(N) = 20cm [H times N is equal to 20 cm]

and

(H)(S) = 6cm [H times S is equal to 6 cm]

then what does

(N)(S) = ? [N times S equals what?]

since H is used in both equations, we know they are the same number, so H has to be a number that is a factor (meaning what are the individual numbers in a multiplication equation)

Since (H)(N) = 20 H represents one of the individual numbers. And the factors of 20  are (1, 2, 4, 5, 10. 20)

Since (H)(S) = 6 H represents one of the individual numbers. And the factors of 6 are (1, 2, 3, 6)

The only number that is the same in each group of factors is 2

So H = 2. Now we can replace H with the number 2

(H)(N)=20 is (2)(N) = 20; Then you divide both sides by 2 and you get

(2)(N)/2 = 20/2 ; the 2 on the left side cancel each other and 20/2 = 10

N =10

You do the same process for (H)(S) = 6

(2)(S) = 6

(2)(S)/2 = 6/2

S = 3

(N)(S) = ?

(10)(3) = 30 cm

so 30 cm is the answer

Answer:

The answer should be A.) (0,2) and D.) (3,0)

Step-by-step explanation:

Hope i helped.

A brainliest is always appreciated.

The dimensions of the rectangular slab are 16 meters in length and 2 meters in width.

Let's assume the length of the rectangular slab of concrete is L meters. According to the given information, the width is 14 meters less than the length, so the width would be L - 14 meters.

The formula for the area of a rectangle is A = length × width. In this case, the area is given as 32 m², so we can set up the equation:

32 = L × (L - 14)

Expanding the equation, we get:

32 = L² - 14L

Rearranging the equation, we have:

L² - 14L - 32 = 0

To solve this quadratic equation, we can either factorize it or use the quadratic formula. In this case, it's easier to use the quadratic formula:

L = (-b ± √(b² - 4ac)) / (2a)

Here, a = 1, b = -14, and c = -32. Substituting these values into the formula, we get:

L = (14 ± √((-14)² - 4 × 1 × (-32))) / (2 × 1)

Simplifying further:

L = (14 ± √(196 + 128)) / 2

L = (14 ± √324) / 2

L = (14 ± 18) / 2

Therefore, we have two possible values for L:

L₁ = (14 + 18) / 2 = 16

L₂ = (14 - 18) / 2 = -2

Since the length of the slab cannot be negative, we discard the negative value.

Thus, the length of the rectangular slab is 16 meters. To find the width, we subtract 14 meters from the length:

Width = 16 - 14 = 2 meters

Therefore, the dimensions of the rectangle are 16 meters by 2 meters.

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Answer:

\(3\)

Step-by-step explanation:

\(\mathrm{Let\ the\ age\ of\ Sophia\ be\ }x\mathrm{\ and\ age\ of\ Mohal\ be\ }x+2.\\\mathrm{Given,}\\\mathrm{Product\ of\ their\ ages = 15}\\\mathrm{or,\ }x(x+2)=15\\\mathrm{or,\ }x^2+2x=15\\\mathrm{or,\ }x^2+2x-15=0\\\mathrm{or,\ }x^2+5x-3x-15=0\\\mathrm{or,\ }x(x+5)-3(x+5)=0\\\mathrm{or,\ }(x+5)(x-3)=0\\\mathrm{i.e.}\ x=-5\ \mathrm{or}\ 3.\)

\(x=-5\ \mathrm{is\ disgarded\ because\ age\ cannot\ be\ negative.}\\\mathrm{So\ the\ age\ of\ Shopia,\ }x=3\)

The coefficient in the expression is 5.

A coefficient is a numerical value that is multiplied by a variable in an algebraic expression.

In a polynomial expression, coefficients can be the numbers in front of the variables. The coefficient determines the size and direction of the variable's effect on the expression as a whole. For example, in the expression 2x, the coefficient is 2.

Therefore, the coefficient in the expression 10 – 6 + 5n is 5.

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Answer: 5

Step-by-step explanation:

Answer:

130

Step-by-step explanation:

Answer:

130

Step-by-step explanation:

The closest multiple of 10 is 130

Answer:

the approximate population density of South America is 1.97 × 10^1 people per square kilometer.

Step-by-step explanation:

To find the population density of South America, we need to divide its population by its area:

Population density = Population / Area

Plugging in the given values:

Population density = 3.50 × 10^8 / 1.78 × 10^7

Population density = 19.66

To express the answer in standard form, we need to move the decimal point one place to the left and adjust the exponent accordingly:

Population density = 1.966 × 10^1

Rounding this to the nearest hundredth gives:

Population density ≈ 1.97 × 10^1

Therefore, the approximate population density of South America is 1.97 × 10^1 people per square kilometer.

The given statement is Four less than a number is nine.

Remember that "less than" refers to subtraction. "A number" refers to a variable x. "is" refers to equality. So, the expression would be

Answer: p=50 h=2

Step-by-step explanation:

so its 50 x 2=100 is the answer then u add 3

Answer:

1 cubic meter equals 1000 liters

Step-by-step explanation:

i think this is right