The total amount of money in a savings account after t years is given by the function A=1000(1.023)^t .

How could this function be rewritten to identify the monthly interest rate?

What is the approximate monthly interest rate?



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Function Monthly interest rate

A = 1000(1 + 0.023)^12t

A = 1000(1.023^12)^t/12

A = 1000(1.023^t/12)^12t

0.23%

0.19%

0.31%

Generally, whenever a point (x,y) is reflected across the y axis, the y coordinate stays the same and the sign of x coordinate changes.

So [tex](x,y)[/tex] changes to [tex](-x,y)[/tex].

Point D in the diagram shown has coordinates [tex](3,-1)[/tex]. According to the rule, the x-coordinate, 3, will change to -3 and the y-coordinate, -1, would stay the same.

Hence, our image of D after the reflection about y-axis would have coordinates [tex](-3,-1)[/tex].

ANSWER: [tex](-3,-1)[/tex]

Answer:

(-3, -1)

Step-by-step explanation:

To prove that BH = CK in triangle ABC, we can use the angle bisector theorem. The theorem states that the angle bisector of an angle in a triangle divides the opposite side into two segments proportional to the other two sides. By applying this theorem and representing BH as x and CK as y, we can show that x = y, thus proving that BH = CK.

In triangle ABC, to prove that BH = CK, we can use the angle bisector theorem. Since m∠B = m∠C, the angle bisector of ∠B will divide the side AC into two segments proportional to the other two sides. Let's denote BH as x and CK as y. According to the angle bisector theorem, we have:

Since AB = AC (isosceles triangle), we can rewrite the first equation as:

x / BC = AH / HC

And the second equation as:

AC / BC = AK / y

Since AB = AC, we can substitute AC with AB:

x / BC = AK / y

Now, we can cross-multiply and solve for x and y:

x * BC = AK * HC

y * BC = x * HK

Simplifying, we get:

x = AK * HC / BC

y = x * HK / BC

Since HK = HC, we have:

x = AK

y = x

Therefore, BH = x = CK = y.

Answer:-  2. ∠JKM≅∠LKM

5. MK≅MK

6. AAS congruence postulate.

7. Corresponding parts of congruent triangles are congruent.

8. Definition of equidistant.

Therefore the complete proof will be

Proof :- 1. KM is the line bisector of ∠JKL.  [Given]

2. ∠JKM≅∠LKM             [Definition of bisector]

3. ∠KXM and ∠KYM are right angles [Given]

4. ∠KXM ≅ ∠KYM [All right angles are congruent]

5. MK≅MK  [reflexive property of congruence]

6. ΔKXM ≅ ΔKYM  [AAS congruence postulate]

7. MX≅MY [Corresponding parts of congruent triangles are congruent]

8. Point  M is equidistant from the sides of ∠JKL [Definition of equidistant]

Hence proved.

divide 714 by 12

714 / 12 = 59.5 spools per week

an equation of the line passing through point P(0, 0) that is perpendicular to the given line is

[tex]y=\frac{1}{9} x[/tex]

Given :

the line passing through point P(0, 0) that is perpendicular to the line

y = −9x−1

The given equation is in the form of y=mx+b

where m is the slope and b is the y intercept

Find out slope from the given equation y=-9x-1

Slope of the given equation is -9

Slope of perpendicular lines are negative reciprocal of one another

slope of perpendicular line is negative reciprocal of -9 is [tex]\frac{1}{9}[/tex]

slope of perpendicular line m=[tex]\frac{1}{9}[/tex]

The line passes through the point (0,0) that means y intercept is 0

the value of b=0

[tex]m=\frac{1}{9} , b=0\\y=mx+b\\y=\frac{1}{9} x+b\\y=\frac{1}{9} x[/tex]

an equation of the line passing through point P(0, 0) that is perpendicular to the line y = −9x−1 is

[tex]y=\frac{1}{9} x[/tex]

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The equation of the line passing through point P(0, 0) and perpendicular to the line y = -9x-1 is y = (1/9)x, with the slope of the line being the negative reciprocal of -9.

To write an equation of the line passing through point P(0, 0) that is perpendicular to the line y = −9x−1, we first identify the slope of the given line. The slope of the line y = −9x−1 is −9, so the slope of a line perpendicular to it will be the negative reciprocal. Therefore, the perpendicular slope is 1/9.

Since the point P(0, 0) is also the y-intercept, we can directly write the equation of the perpendicular line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Thus, the equation of the line we are looking for is y = (1/9)x.

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Answer:

Range.

Step-by-step explanation:

Alan must use the measure called Range, which indicates the dispersion between the extreme values of a variable. It is calculated as the difference between the highest and the lowest value of the variable. It is denoted as R. First the data is sorted, then it is calculated as:

R = x (n) - x (1) where,

x (n): It is the largest value of the variable.

x (1): It is the smallest value of the variable.

In the given case (5, 6, 7, 5, 7, 9, 2, 4, 8, and 7), we sort the data, and get,

2, 4, 5, 5, 6, 7, 7, 7, 8, 9

x (n) = 9

X (1) = 2

R = 9 - 2 = 7

Hope this helps!

The x-intercepts of the graphed function are -2, -1, 1, and 2

The x-intercept is the point where the graph crosses the x-axis

This means that the point on the x-axis where y = 0

From the graph, we have:

x = -2, -1, 1, and 2 when y = 0

Hence, the x-intercepts of the graphed function are -2, -1, 1, and 2

Read more about x-intercepts at:

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The required equation of the line is y = 3x which passes through the origin with the slope 3.

The slope of the line is defined as the gradient of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

We have to determine the equation of the line that passes through the origin with slope 3.

Let's assume slope-intercept form:

So required line in the slope-intercept form is:

y = mx + b

where m is the slope and b is the y-intercept.

In this case, the slope of line m = 3, and the line passes through the origin

So, therefore equation will be:

y = 3x + 0 or

y = 3x

Thus, the required equation of the line is y = 3x which passes through the origin with the slope 3.

Learn more about the Slope of Line here:

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1. less than  ( I gave x a number and did both equations )

2. the equation = 400 which is greater than 35

Answer:

80%

Step-by-step explanation:

Let us suppose x percent of Bill's salary is equal to Jacks's salary.

Thus, we can write

x% of 87.50 = 70

Mathematically, we can write this as

[tex]0.0x\times87.50=70[/tex]

Solve the equation for x

[tex]0.0x=\frac{70}{87.50}\\\\x=\frac{70}{87.50}\times100\\\\x=80[/tex]

Therefore, Jack's salary is 80% of Bill's salary

The answer is:

$609.39

Answer: So, the required inequality that can be used to represent this situation is [tex]2x+3\leq 31[/tex]

Step-by-step explanation:

Let the age of Catie's brother be 'x'.

Let the age of Catie be 'x+3'.

According to question, the sum of their ages is no more than 31.

So, it becomes,

[tex]x+x+3\leq 31\\\\2x+3\leq 31[/tex]

So, the required inequality that can be used to represent this situation is

[tex]2x+3\leq 31[/tex]

Answer:

The answer is [tex]9[/tex]

Step-by-step explanation:

we have

[tex](243)^{\frac{2}{5}}[/tex]

we know that

[tex]a^{\frac{n}{m}}=\sqrt[m]{a^{n}}[/tex]

so

[tex](243)^{\frac{2}{5}}=\sqrt[5]{243^{2}}[/tex]

Remember that

[tex]243=3^{5}[/tex]

Substitute

[tex]\sqrt[5]{243^{2}}=\sqrt[5]{(3^{5})^{2}}\\ \\= \sqrt[5]{(3^{10})}\\ \\=3^{\frac{10}{5}}\\ \\= 3^{2} \\ \\=9[/tex]

Answer:

29 4/25 square inches (not given in the options)

Step-by-step explanation:

A square is a plain 4 sided shape with equal sides. As such, all sides of a square are equal. If the length o a side of a square is s, the area of the square will be s² while the perimeter will be 4s.

Area of square = (5 2/5 inches)²

= (27/5 inches)²

= 729/25 square inches

= 29 4/25 square inches