Solve the inequality and graph the solution
4x-5>7

Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)

To rotate a point 90 degrees  clockwise about a given point,we can follow these steps -

Translate the coordinates   of the given point so that the center of rotation is at the origin.   In this case,we subtract the coordinates   of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).

Perform the rotation by swapping the x and y coordinates and changing the sign of the   new x coordinate. In this case,we  swap the x and y coordinates of (-5, 3)   to  get (3, -5).

Translate the coordinates back to their original position   by adding the coordinates of the center (0,1)  to the result from step 2. In   this case, we add (0,1) to (3, -5) to get (3, -4).

Therefore, the coordinates   of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).

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Step-by-step explanation:

The transformation y = sin(2x) affects the graph of y = sin(x) by compressing it horizontally.

The function y = sin(2x) has a coefficient of 2 in front of the x variable. This means that for every x value in the original function, the transformed function will have half the x value.

To see the effect of this transformation, let's compare the graphs of y = sin(x) and y = sin(2x) by plotting some points:

For y = sin(x):

x = 0, y = 0

x = π/2, y = 1

x = π, y = 0

x = 3π/2, y = -1

x = 2π, y = 0

For y = sin(2x):

x = 0, y = 0

x = π/2, y = 0

x = π, y = 0

x = 3π/2, y = 0

x = 2π, y = 0

As you can see, the y-values of the transformed function remain the same as the original function at every x-value, while the x-values of the transformed function are compressed by a factor of 2. This means that the graph of y = sin(2x) appears narrower or more "squeezed" horizontally compared to y = sin(x).

Therefore, the correct statement is: It is compressed horizontally.

Answer:

y = (-1/19)(x - 8)² + 1521/76

Step-by-step explanation:

A parabola moves in such a way that it's distance from it's focus and directrix are always equal.

Now, we are given that directrix is y = 9.75 and focus is at (8, 0.25). Focus can be rewritten as (8, ¼) and directrix can be rewritten as y = 39/4

If we consider a point with the coordinates (x, y), it means the distance from this point to the focus is;

√((x - 8)² + (y - ¼)²)

Distance from that point to the directrix is; (y - 39/4)

Thus;

√((x - 8)² + (y - ¼)²) = (y - 39/4)

Taking the square of both sides gives;

((x - 8)² + (y - ¼)²) = (y - 39/4)²

(x - 8)² + y² - ½y + 1/16 = y² - (39/2)y + (39/4)²

Simplifying this gives;

(x - 8)² - (39/4)² = (½ - 39/2)y

(x - 8)² - 1521/4 = -19y

(x - 8)² - 1521/4 = -19y

Divide both sides by -19 to get;

y = (-1/19)(x - 8)² + 1521/76

Answer:

Step-by-step explanation:

Tak

Answer:

\(\boxed{1\dfrac{1}{2}\;miles}\)

Step-by-step explanation:

Convert 1 9/10 to an improper fraction and then the calculation becomes simpler

\(1 \dfrac{9}{10 } = \dfrac{ 1 \cdot 10 + 9}{10} = \dfrac{19}{10}\\\\\)

Since Will has already walked 2/5 of a mile to the park, the remaining distance

\(= \dfrac{19}{10} - \dfrac{2}{5}\\\\\)

Make the denominators the same by multiplying both the numerator and denominator of 2. This does not change the original value of 2/5

\(\dfrac {2 \times 2}{5 \times 2} = \dfrac{4}{10}\\\\\)

Therefore the remaining distance is

\(\dfrac{19}{10} - \dfrac{2}{5}\\\\\\= \dfrac{19}{10} - \dfrac{4}{10}\)

Since the denominator is the same we can simply subtract the numerator terms and use 10 as the denominator for the result:

\(= \dfrac{19-4}{10} = \dfrac{15}{10} \\\\\)

Dividing numerator and denominator by 5 reduces it to the lowest fraction

\(\dfrac{15 \div 5}{10 \div 5} = \dfrac{3}{2} = 1\dfrac{1}{2} \\\\\)

So Will needs to travel a further \(1\dfrac{1}{2}\) miles to reach the park

Answer:

Step-by-step explanation:

From the first question:

We are to find PV of the annuity.

Using the formula:

Present value of Annuity  = Annuity Amount × Present Value Annuity Factor i.e. PVAF (n , r)

Where , Annuity Amount = $4,000            

n = No. of periods = 7 years × 4 quarters per year = 28 periods but since the first payment is at beginning of the quarter, Then, n = 27 when considered for PVAF

r  = 6.2% / 4 quarters = 1.55%,

PVAF(n0,r) when first payment is at beginning of n i.e. n0 = 1 + { [1-(1+r)^ -n0 ]/r }

= 1 + { [1-(1+0.0155)^ {-27}]/0.0155 }

= 1 + [ (1 - 0.66015 ) ] / 0.0155]

= 1 + 21.926

= 22.926

PVAF(28,1.55%) = 22.926

Thus , Present Value of Annuity = $4,000 × 22.926  = $91704.00

2. Present value of Annuity due = Annuity Amount × Present Value Annuity Factor i.e. PVAF (n , r)

Present Value of Annuity  = $90,000

n = No. of periods = 7.5 years × 4 quarters per year = 30 periods

r  = 5.4% / 4 quarters = 1.35%,

PVAF(n,r) = [1-(1+r)^-n]/r

PVAF(n,r) = [1-(1+0.0135)^ -30]/0.0135

PVAF(30,1.35%) = (1 - 0.6688)/0.0135

PVAF(30,1.35%) = 0.3312/0.0135

PVAF(30,1.35%) = 24.53

Hence ;

$90,000 = Annuity Amount × 24.53

Annuity amount = $90,000/24.53 = $3,668.48

The equation of a circle is written as (x – h)^2 + (y – k)^2 = r^2

h and k are the center point and r is the radius.

In the given equation h = -6 and k = 7 and r would be the square root of 81, which is 9.

Center (-6,7)

Radius = 9

The required center is \((-6,7)\) and the radius is 9 units.

Given equation is,

\((x + 6)^2 + (y-7)^2 = 81\)....(1)

Equation of the circle: The general equation of the circle with the center (a,b) and the radius r is represented by,

\((x-a)^2+(y-b)^2=r^2\)...(2)

We can write the given equation as,

\((x + 6)^2 + (y-7)^2 = (9)^2\)

Comparing equations (1) and (2) we get,

The Centre of the given circle is \((-6,7)\)

The radius of the given circle is 9 units.

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Answer:

Scott ran 5 miles

Step-by-step explanation:

22-17=5

Reasonableness...

5+17=22

Answer: 39 <3 ^_^

Step-by-step explanation: Last week Asanji ran 17 miles more than Scott. Asanji ran 22 miles. How many miles did Scott run? 17+22=

Answer:

width(w)= 20inches

Step-by-step explanation:

solution,

given,

perimeter of a rectangle (P)=68inches

length of rectangle= 14 inches

we know,

perimeter of a rectangle=2L + 2W

or,68=2×14+2×w

or,68-28=2w

or,40=2w

or,w=40÷2

or,w=20inches.

Answer:

4

Step-by-step explanation:

The statement means that there are 4 "groups"(stars) of 5 "items"(points), so there are 4 groups.

There were 4 stars and 5 points on each star we gets, The groups were there 4.

We have given that,

There were 4 stars and 5 points.

Any combination of a finite number of the operations of addition, multiplication, subtraction, and division

We have to determine How many groups were there

The statement means that there are 4 groups(stars) of 5 items(points), so there are 4 groups.

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Answer:

12p + 8q

Step-by-step explanation:

Answer: 154cm

Step-by-step explanation:

10% of 140 is 14

add that 10% to get 154

The equation of the line that passes through the points (1,6) and (2,7) is y = x + 5.

We can use the point-slope version of the equation, which is: to determine the equation of a line passing through two specified points.

y - y₁ = m(x - x₁)

where (x₁, y₁) are the coordinates of one of the points, m is the slope of the line, and (x, y) are the coordinates of any other point on the line.

Use the points (1,6) and (2,7) to find the equation of the line:

Using (x₁, y₁) = (1,6):

y - 6 = m(x - 1)

Now, substitute the coordinates (2,7) into the equation:

7 - 6 = m(2 - 1)

1 = m

So, the slope of the line is m = 1.

Substitute this value into the equation:

y - 6 = 1(x - 1)

y - 6 = x - 1

y = x + 5

Therefore, the equation of the line that passes through the points (1,6) and (2,7) is y = x + 5.

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Check the picture below.

so the parabolic path of the object is more or less like the one shown below in the picture, now this object has an initial of 1240 ft, as it gets thrown from the ski lift, so from 0 seconds is already higher than 1000 feet.

\(h=-16t^2+32t+1240\hspace{5em}\stackrel{\textit{a height of 1000 ft}}{1000=-16t^2+32t+1240} \\\\\\ 0=-16t^2+32t+240\implies 16t^2-32t-240=0\implies 16(t^2-2t-15)=0 \\\\\\ t^2-2t-15=0\implies (t-5)(t+3)=0\implies t= \begin{cases} ~~ 5 ~~ \textit{\LARGE \checkmark}\\ -3 ~~ \bigotimes \end{cases}\)

now, since the seconds can't be negative, thus the negative valid answer in this case is not applicable, so we can't use it.

So the object on its way down at some point it hit 1000 ft of height and then kept on going down, and when it was above those 1000 ft mark  happened between 0 and 5 seconds.

That’s easyyyyy

Step-by-step explanation:

It’s 62...

:)

Answer:

62 :)

Step-by-step explanation:

Answer:

Statement 1 is false, statement 2 is true.

Step-by-step explanation:

The triangle has been dialated by a scale factor of 2.5

The exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8) is, 3 / 5

We have to given that;

the terminal side of theta in standard position contains the point (6,-8)

Hence, For given condition we get;

The exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8) is,

Here, x = 6, y = - 8

Hence, We get;

r = √x² + y²

r  = √6² + 8²

r = √36 + 64

r = √100

r = 10

So, The exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8) is,

cos θ = x / r

cos θ = 6 / 10

cos θ =  3 / 5

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Answer:

I believe that the answer is D.

Step-by-step explanation:

Hope this helps!

Answer:

nearest ten thousand – 2,620,000

nearest hundred thousand – Two million, six hundred thousand

Step-by-step explanation:

hope this helps.

Answer:WHAT DOES THAT EVEN MEAN!?!?

Step-by-step explanation:

!!!!!!!!

Answer:

\(9w^{2}\)

Step-by-step explanation:

An easy way to find the GCF of different numbers is to list out all of their factors. In this case, the coefficients share multiple factors, but the largest is 9.

Additionally, when dividing variables with different powers you subtract the exponents. So, if you were to divide \(\frac{w^3}{w^2}\) the final answer would be \(w\) because 3-2 is 1. So, to find the GCF of like variables find the biggest number that can be subtracted from all of them. In this case, that is 2; therefore, the GCF of the variables is \(w^2\). Put the 2 parts together for the final answer \(9w^{2}\).

Hello!

I'll explain this exercise to you with some examples to make it clear.

First, let's imagine a square A with sides of 6cm, and a square B with sides of 4 cm:

Let's calculate the areas of both squares, using the formula:

Square A:

Square B:

Now, let's calculate the ratio between the areas:

The ratio between the areas will be 36/16.

Answer:

h = 2

Step-by-step explanation:

you know the original rectangle [h = 10, w = 15]

1. The height of 15 inches turned to 3 inches by diving by 5

2. You have to do the same with the height too!

3. 10/5 = 2

The new height is 2 inches.

Answer:

please refer tp the photo . It s D. 101 in2

Step-by-step explanation:

Answer:

(i) x ≤ 1

(ii) ℝ except 0, -1

(iii) x > -1

(iv) ℝ except π/2 + nπ, n ∈ ℤ

Step-by-step explanation:

(i) The number inside a square root must be positive or zero to give the expression a real value. Therefore, to solve for the domain of the function, we can set the value inside the square root greater or equal to 0, then solve for x:

\(1-x \ge 0\)

\(1 \ge x\)

\(\boxed{x \le 1}\)

(ii) The denominator of a fraction cannot be zero, or else the fraction is undefined. Therefore, we can solve for the values of x that are NOT in the domain of the function by setting the expression in the denominator to 0, then solving for x.

\(0 = x^2+x\)

\(0 = x(x + 1)\)

\(x = 0\)     OR     \(x = -1\)

So, the domain of the function is:

\(R \text{ except } 0, -1\)

(ℝ stands for "all real numbers")

(iii) We know that the value inside a logarithmic function must be positive, or else the expression is undefined. So, we can set the value inside the log greater than 0 and solve for x:

\(x+ 1 > 0\)

\(\boxed{x > -1}\)

(iv) The domain of the trigonometric function tangent is all real numbers, except multiples of π/2, when the denominator of the value it outputs is zero.

\(\boxed{R \text{ except } \frac{\pi}2 + n\pi} \ \text{where} \ \text{n} \in Z\)

(ℤ stands for "all integers")

Answer:

(i)  x ≤ 1

(ii)  All real numbers except x = 0 and x = -1.

(iii)  x > -1

(iv)  All real numbers except x = π/2 + πn, where n is an integer.

Step-by-step explanation:

The domain of a function is the set of all possible input values (x-values).

\(\hrulefill\)

\(\textsf{(i)} \quad f(x)=\sqrt{1-x}\)

For a square root function, the expression inside the square root must be non-negative. Therefore, for function f(x), 1 - x ≥ 0.

Solve the inequality:

\(\begin{aligned}1 - x &\geq 0\\\\1 - x -1 &\geq 0-1\\\\-x &\geq -1\\\\\dfrac{-x}{-1} &\geq \dfrac{-1}{-1}\\\\x &\leq 1\end{aligned}\)

(Note that when we divide or multiply both sides of an inequality by a negative number, we must reverse the inequality sign).

Hence, the domain of f(x) is all real numbers less than or equal to -1.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x \leq 1\\\textsf{Interval notation:} \quad &(-\infty, 1]\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \leq 1 \right\} \end{aligned}}\)

\(\hrulefill\)

\(\textsf{(ii)} \quad g(x) = \dfrac{1}{x^2 + x}\)

To find the domain of g(x), we need to identify any values of x that would make the denominator equal to zero, since division by zero is undefined.

Set the denominator to zero and solve for x:

\(\begin{aligned}x^2 + x &= 0\\x(x + 1) &= 0\\\\\implies x &= 0\\\implies x &= -1\end{aligned}\)

Therefore, the domain of g(x) is all real numbers except x = 0 and x = -1.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x < -1 \;\;\textsf{or}\;\; -1 < x < 0 \;\;\textsf{or}\;\; x > 0\\\textsf{Interval notation:} \quad &(-\infty, -1) \cup (-1, 0) \cup (0, \infty)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \neq 0,x \neq -1 \right\} \end{aligned}}\)

\(\hrulefill\)

\(\textsf{(iii)}\quad h(x) = \log_7(x + 1)\)

For a logarithmic function, the argument (the expression inside the logarithm), must be greater than zero.

Therefore, for function h(x), x + 1 > 0.

Solve the inequality:

\(\begin{aligned}x + 1 & > 0\\x+1-1& > 0-1\\x & > -1\end{aligned}\)

Therefore, the domain of h(x) is all real numbers greater than -1.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x > -1\\\textsf{Interval notation:} \quad &(-1, \infty)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x > -1\right\} \end{aligned}}\)

\(\hrulefill\)

\(\textsf{(iv)} \quad k(x) = \tan x\)

The tangent function can also be expressed as the ratio of the sine and cosine functions:

\(\tan x = \dfrac{\sin x}{\cos x}\)

Therefore, the tangent function is defined for all real numbers except the values where the cosine of the function is zero, since division by zero is undefined.

From inspection of the unit circle, cos(x) = 0 when x = π/2 and x = 3π/2.

The tangent function is periodic with a period of π. This means that the graph of the tangent function repeats itself at intervals of π units along the x-axis.

Therefore, if we combine the period and the undefined points, the domain of k(x) is all real numbers except x = π/2 + πn, where n is an integer.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &\pi n\le \:x < \dfrac{\pi }{2}+\pi n\quad \textsf{or}\quad \dfrac{\pi }{2}+\pi n < x < \pi +\pi n\\\textsf{Interval notation:} \quad &\left[\pi n ,\dfrac{\pi }{2}+\pi n\right) \cup \left(\dfrac{\pi }{2}+\pi n,\pi +\pi n\right)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \neq \dfrac{\pi}{2}+\pi n\;\; (n \in\mathbb{Z}) \right\}\\\textsf{(where $n$ is an integer)}\end{aligned}}\)

In general, there were more people per table on Tuesday with 8 number of people per table.

In Mathematics, a dot plot can be defined as a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of dots.

By critically observing the given dot plots which is used to illustrate the numbers of people per table at a bingo hall on two nights, we can reasonably infer and logically deduce that there were more people per table on Tuesday than on Wednesday.

In conclusion, there were 8 number of people per table on Tuesday while there were 5 number of people per table on Wednesday.

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Answer:

C

Step-by-step explanation:

For this, you want to treat i like any other variable, and combine like terms. However you need to keep in mind that there is a negative sign before the second set of parentheses. This means everything inside it should have a negative before it. So we can write it like this:

(7 + 3i) - (3 - 9i)

7 + 3i -3 +9i

4 + 12i

Hope that helps!