Rectangle ABCD and A’B’C’D’ are similar.

a. What is the scale factor from ABCD to

A’B’C’D’?

b. What is the scale factor from A’B’C’D’ to

ABCD?

ans. 1400000

we know that

work done by gravity =  mgh

just putting values we get

= 1400x 100 x 10

= 1400000

hence,work done an elevator motor need to do to lift a 1400kg elevator a height of 100m is 1400000

Using the continuously compounded interest formula, the amount of debt owed after 5 years is $ 8988.18

The continuous compounding interest formula is given by P = Peⁿˣ where

Since Edgar accumulated $7,000 in credit card debt. If the interest rate is 50% per year and he does not make any payments for 5 years, how much will he owe on this debt in 5 years by compounding continuously? To determine that, we use the continuously compounded interest formula.

Given that

Substituting the values of the variables into the equation, we have that

P = Peⁿˣ

P = $7000e⁰°⁵ ˣ ⁵

P = $7000e⁰°²⁵

P = $7000(1.28)

P = $ 8988.18

So, the amount of debt owed is $ 8988.18

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The value of p is -3/2, the value of q is -1/(t+1), and the value of r is 2.

Let the first term of the arithmetic series be a, and the common difference be d = 3. Then, we have:

a = 2t + 1

n-th term = a + (n-1)d = 2t + 1 + 3(n-1) = 3n + (2t - 2)

(Notice that the second equation can be found by substituting the expression for a into the formula for the n-th term and simplifying.)

We also know that the n-th term is given by (14t - 5), so we can equate the two expressions:

3n + (2t - 2) = 14t - 5

Simplifying and solving for n, we get:

n = (12t + 3)/3 = 4t + 1

So, the n-th term can also be expressed as:

3n + (2t - 2) = 3(4t + 1) + (2t - 2) = 14t - 5

Simplifying, we get:

14t - 5 = 14t - 5

This confirms that our expressions for the first term, common difference, and n-th term are all consistent with each other.

Now, we can use the formula for the sum of an arithmetic series to find the sum of the first n terms:

S_n = (n/2)(2a + (n-1)d) = (n/2)(4t + 4t + 1 + 3n - 3) = (3/2)n^2 + (5/2)t - 3n/2 + 1/2

We want to rewrite this expression in the form p(qt - 1)^r. To do this, we can try to complete the square in the n term, like this:

S_n = (3/2)[n^2 - 2n(t+1) + (t+1)^2] + (5/2)t - (3/2)(t+1)^2 + 1/2

S_n = (3/2)[n - (t+1)]^2 - (1/2)(t+1)^2 + (5/2)t + 1/2

Let u = n - (t+1), so that:

S_n = (3/2)u^2 - (1/2)(t+1)^2 + (5/2)t + 1/2

We want to rewrite this in the form p(qt - 1)^r, so let's try to match the terms:

p = -3/2

q = -1/(t+1)

r = 2

Therefore, the value of p is -3/2, the value of q is -1/(t+1), and the value of r is 2.

Note that the assumption that t is greater than 0 was not necessary for the derivation of the sum formula, but it is necessary for the existence of the arithmetic series (since otherwise the first term would be negative).

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The text format of the question in the picture:

22. The first term of an arithmetic series is (2t + 1) where t is > 0 The nth term of this arithmetic series is (14t - 5)

The common difference of the series is 3

The sum of the first n terms of the series can be written as p(qt - 1)^r where p, q and r are integers.

Find the value of p, the value of q and the value of r Show clear algebraic working.

Answer:

Step-by-step explanation:

There are 2 parts for your function.    (see image)

y=4x, which is a line with a slope of 4 but x≠0, so there is a hole there

y=1 only at x=0  so the point is above the line

(a)  Domain: All real numbers.  There is a value for all x's

(b)  There is no x-intercept because the graph never touches x

y-intercept (1,0)  That's where the graph touch y

(c) see image

(d) range:  (-∞, 0) U (0, +∞)   there is a stop at 0 for y values

can also be written   -∞<x<1  and 1<x<+∞

(e) yes it's continuous for domain but not range.   because even though there is a jump at that point, i still have an x value.  The jump causes me to not have a y value at y=0, that's why range is discontinuous

Answer:

To write the Hindu-Arabic numeral 872 as a Babylonian numeral using the symbols I and <, we need to break it down into its place values:

The digit 8 is in the hundreds place.

The digit 7 is in the tens place.

The digit 2 is in the ones place.

To represent 800 in the hundreds place, we use 8 symbols <. To represent 70 in the tens place, we use 7 symbols < followed by 1 symbol I. To represent 2 in the ones place, we use 2 symbols I.

Putting these symbols together, we get the Babylonian numeral:

<<<<< <<<< <<<< <<<< IIII

So, the Babylonian numeral equivalent of the Hindu-Arabic numeral 872 is <<<<< <<<< <<<< <<<< IIII.

Answer:

The p-value is the probability of observing a test statistic as extreme or more extreme than the observed one, assuming the null hypothesis is true. In this case, since it is a right-tailed test, the p-value is the area to the right of the observed test statistic Z=1.74 under the standard normal distribution curve.

Answer: p > 6.5

Step-by-step explanation:

Let p = the time, in hours, that Harry plans to practice soccer.

Since we don't know the hours Harry will plan to practice soccer, we will replace it with p, and Harry wants to practice more than his older brother, so we put the greater than symbol.

Hope this helped!

Answer:

  x < -1 or x ≥ 5

Step-by-step explanation:

You want the solution and its graph for the compound inequality ...

Adding 2 to the first inequality gives ...

  3x < -3

  x < -1 . . . . . divide by 3

Multiplying the second inequality by -1/2 gives ...

  x ≥ 5

The solution is x < -1 or x ≥ 5.

By using the corresponding angles, vertically opposite angles, alternate interior angles, and linear pair theorems, the measure of the angles are:

m ∠1 = 39°

m ∠2 = 141°

m ∠3 = 141°

m ∠4 = 39°

m ∠5 = 39°

m ∠6 = 141°

m ∠7 = 39°

From the question, we are to calculate the measure of the unknown angles in the given diagram

By the Linear pair theorem,

We can write that

m ∠5 + 141° = 180°

Thus,

m ∠5 = 180° - 141°

m ∠5 = 39°

Likewise

m ∠7 + 141° = 180°

m ∠7 = 180° - 141°

m ∠7 = 39°

By the vertical angles theorem,

We can write that

m ∠6 = 141° (Vertically opposite angles)

By the corresponding angles theorem,

We can write that

m ∠2 = 141° (Corresponding angles)

m ∠2 = m ∠3 (Vertically opposite angles)

Therefore,

m ∠3 = 141°

m ∠4 = m ∠5 (Alternate interior angles)

m ∠4 = 39°

m ∠1 = m ∠4 (Vertically opposite angles)

Therefore,

m ∠1 = 39°

Hence,

The measure of angle 1 is 39°

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The number of roof trusses that would be needed for the longest length is 2

The longest lengths from the question are given

Longest lengths = 28 and 22

Next, we expand the lengths of the roof trusses

This is to calculate the greatest common factor (GCF) of the lengths

So, we have

28 = 2 * 2 * 7

22 = 2 * 11

Multiplying the common factors gives the GCF

So, we have

GCF = 2

This means that the number of roof trusses that would be needed for the longest length is 2

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Answer:

I'm pretty much confused abt this one bc I didn't get an exact answer. Anyway I think it's 13.1

Step-by-step explanation:

The pic

Answer:

21 and 42

Step-by-step explanation:

Lets say x and y are our numbers. x is the smaller number, y is the larger.

We can construct the equations:

x = 0.5y

x + y = 63

Substitute 0.5y for x in the second equation.

0.5y + y = 63

1.5y = 63

y = 42.

Plug y into the first equation.

x = 0.5 * 42

x = 21.

Your numbers are 21 and 42.

The exact values for both equations are as follows:

a) 3

b) -√3/2 - √2/2

a) In order to ascertain the precise value of 4sin(π/6) + tan(π/4), we must first evaluate the trigonometric functions involved: sin(π/6) = 1/2 and tan(π/4) = 1.

Now, by substituting these values in the equation, we get

4(1/2) + 1 = 2 + 1 = 3.

b) To calculate cos(4π/3) tan(330°) - sin(3π/4), it is necessary to convert 330° into radians: (330 * π) / 180 = 11π/6.

After setting this conversion, evaluate the trigonometric functions present: cos(4π/3) = -1/2, tan(11π/6) = √3, and sin(3π/4) = √2/2.

When these values are used within the equation, the result is (-1/2)(√3) - (√2/2) which equals -√3/2 - √2/2.

Ergo, the exact values for both equations are as follows:

a) 3

b) -√3/2 - √2/2

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A graph of the functions with the asymptotes is shown in the image below.

The pre-image of the function y = log₂(x + 1) was horizontally shifted to the left by 1 unit.

The pre-image of the function y = log₂(x) + 4 was vertically shifted up by 4 units.

In Mathematics, the translation a geometric figure or graph to the left means subtracting a numerical value to the point on the x-coordinate of the pre-image;

g(x) = f(x + N)

In Mathematics and Geometry, the translation a geometric figure upward means adding a numerical value to the point on the positive y-coordinate (y-axis) of the pre-image;

g(x) = f(x) + N

Since the parent function f(x) was horizontally translated 1 unit left, we have the following transformed function;

y = log₂(x + 1)

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The answer is 11 or at least i think it is

Answer:

Step-by-step explanation:

14+12 = 26+8 = 34 + 6 is 40

the answer is 40.

Answer:

[tex]2\sqrt{10[/tex]

Step-by-step explanation:

Add all the numbers together on your calculator

The expression 0 + 10 = 10 is an examle of the identity property of 0

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

The list of options

The identity property of 0 states that

A number added to 0 equals to the number

Mathematically, we have

a + 0 = 0

The options are not clear

So, I will give another example of this property

The expression 0 + 10 = 10 is an examle of the identity property of 0

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Answer: The Answer is NONE

Step-by-step explanation:

The test for polar symmetry is to replace θ with −θ and check if the equation remains the same. If it does, then the polar equation is symmetric about the polar axis. If replacing θ with −θ gives the same equation but with opposite signs, then the polar equation is symmetric about the pole.

Let's apply this test to the given equation:

r = 4cos^2 θ − 3sinθ + 5θ

Replacing θ with −θ, we get:

r = 4cos^2(−θ) − 3sin(−θ) + 5(−θ)

r = 4cos^2 θ + 3sinθ − 5θ

Since the two equations are not the same, we can conclude that the polar equation does not have polar symmetry about the pole or the polar axis.

Therefore, the answer is "none".

The possible values of [tex]$a_{10}$[/tex] are [tex]$-\frac{263}{4}$[/tex]and [tex]$-\frac{13}{5}$[/tex].

Since [tex]$a_1, a_2, a_3,\dots$[/tex] is an arithmetic sequence, we can write[tex]$a_3 = a_1 + d$[/tex] and [tex]$a_5 = a_1 + 2d$[/tex] where [tex]$d$[/tex] is the common difference between consecutive terms. Then the given equations become[tex]$3a_1 + 4d = -12$ and $a_1(a_1 + d)(a_1 + 2d) = 80$.[/tex] Simplifying the second equation gives $a_[tex]1^3 + 3da_1^2 + 2d^2a_1 - 80 = 0$.[/tex]

We can solve for [tex]$d$[/tex] in the first equation: [tex]$d = \frac{-3a_1-12}{4} = -\frac{3}{4}a_1 - 3$[/tex]. Substituting this into the second equation yields a cubic equation in terms of[tex]$a_1$[/tex]:

[tex]a\frac{3}{1}-[/tex] [tex]\frac{9}{4} a\frac{2}{1} -[/tex] [tex]\frac{15}{4} a_{1}- 80=0[/tex]

Using synthetic division or another method, we can find that [tex]$a_1 = -5$[/tex] is a root of this equation. Dividing by [tex]$a_1 + 5$[/tex] yields the quadratic [tex]$a_1^2 - \frac{1}{4}a_1 - 16 = 0$[/tex], which has roots [tex]$a_1 = -4$[/tex] and [tex]$a_1 = 4/5$[/tex].Therefore, the possible values of the common difference [tex]$d$[/tex] are [tex]$-\frac{27}{4}$[/tex] and [tex]\frac{4}{5}$[/tex]

Using [tex]$a_1 = -5$[/tex] and [tex]$d = -\frac{27}{4}$[/tex], we find that [tex]$a_{10} = a_1 + 9d = -5 - \frac{243}{4} = -\frac{263}{4}$.[/tex]

Using [tex]$a_1 = -5$[/tex] and [tex]$d = \frac{4}{5}$[/tex], we find that [tex]$a_{10} = a_1 + 9d = -5 + \frac{36}{5} = -\frac{13}{5}$.[/tex]

Therefore, the possible values of [tex]$a_{10}$[/tex] are [tex]$-\frac{263}{4}$[/tex]and [tex]$-\frac{13}{5}$[/tex].

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The equation of the quadratic function g whose graph is shown above is g(x) = -(x + 4)² - 4

In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:

f(x) = a(x - h)² + k

Where:

Based on the information provided about the vertex and other points, we can determine the value of a as follows:

g(x) = a(x - h)² + k

-13 = a(-7 + 4)² - 4

-13 = a(-3)² - 4

-13 + 4 = 9a

-9 = 9a

a = -1.

Therefore, the required quadratic function is given by:

g(x) = a(x - h)² + k

g(x) = y = -(x + 4)² - 4

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Answer: y = 3/5x - 2/5

Step-by-step explanation: The slope-intercept form is y = mx+b. Hence, solve for y. 3x - 5y = 2.

Move 5y to the right side and move 2 to the left. 3x - 2 = 5y. Divided 5 for all sides: 3/5x - 2/5 = y. Hence, writing in slope-intercept form is y= mx + b, y = 3/5x - 2/5.

The measure of <RTV = 1/2 * (99 - 45) = 27 degrees

Geometrically speaking, a secant is an intersecting line that marks two separate points on the circumference of a circle.

Primarily, it serves as a chord drawn across the diameter which transverses through each endpoint connecting them. The magnitude of the secant is determined by the distance between these intersectional points. This particular element of geometry has various applications in trigonometry, particularly in computing angles and lengths within circles.

According to the Exterior Angle of a Circle Theorem, the measure of an exterior angle of a circle formed by two secants is equal to half the difference of the measures of the intercepted arcs:

Using this theorem,

Thus, the measure of ∠RTV is given as 27

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The value of the variable x is -4

First, we need to know that line segments are described as a section of a line that is bounded by two points or connecting two points.

From the information given, we have that;

Line SA and SD are equal segments

But  SA =3x+19 and SD=5x-11

Now, equate the expressions since they are of equal lengths, we have;

3x + 19 = 5x - 11

collect the like terms

3x - 5x = -11 + 19

Add or subtract the like terms, we have;

-2x = 8

Divide both sides by the coefficient, we have;

x = -4

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As per the given variables, Victor jumped a total of 4 yards.

Total yards jumped = 6 feet high

Additional yards = 2

A yard is one linear yard. "Yd" is the yard symbol. The standard of measurement has always been derived from either a natural item or a portion of the human body, such as a foot, an arm's length, or the width of a hand.

Converting the initial jump of 6 feet to yards, as the additional distance given is also in yards.

There are 3 feet in a yard, therefore -

6 feet = 6/3  

= 2

Thus, Victor jumped 2 yards initially, and then 2 more yards as given in the problem.

Calculating, the total distance Victor jumped in yards -

= 2 + 2

= 4

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Answer:

6

Step-by-step explanation:

To find the highest price Jenny can charge to earn $125 in profit, first write an equation.

total profit = profit per card * number of cards

You want to know when Jenny will earn $125 in profit, and the price per card, x, is the variable. The expression 0.7x represents the profit per card.

125=0.7x(–15x+120)

Now, solve for x. Start by writing the equation in standard form

125=0.7x(–15x+120)

125= –10.5x2+84x

0= –10.5x2+84x–125

Now to solve for x, you can use the quadratic formula with a= – 10.5, b=84, and

So, to the nearest dollar, the highest price Jenny can charge per card to earn $125 in profit is $6.0236 or $6.

46. There are 9 complete doses available from the bottle. 47. There are 8 full doses available in the 120 mL bottle.

Although weight and mass are frequently used interchangeably, they have distinct meanings in the study of physics. Weight is a measurement of the force of gravity acting on an item, whereas mass is a measure of the amount of matter that makes up an object. Weight is typically expressed in newtons (N) or pounds, while mass is typically expressed in kilogrammes (kg) (lb). While an object's mass remains constant, its weight can change depending on how strongly gravity is pulling on it.

46. We know that,

1 fluid ounce = 29.5735 mL

4 fluid ounces = 4 x 29.5735 = 118.294 mL

Each dose is 12.5 mL:

118.294 / 12.5 = 9.46

So there are 9 complete doses available from the bottle.

47. Given, 1 tablespoon is equal to 15 mL.

Thus, doses of 15 mL are in a 120 mL bottle:

120 / 15 = 8

So there are 8 full doses available in the 120 mL bottle.

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Answer:

12

1,2,3,4,5,6,7,8,9,20,11,12

Answer:

Step-by-step explanation: