Graph triangle RST with vertices R(3, 7), S(-5, -2), and T(3, -5) and its image after a reflection over x = -3.​

Answer:

2,160

Step-by-step explanation:

432-324=108 earnings based on sales

sales x 5%=108

sales=108/.05

sales=2,160

Answer:

Let the length of the rectangle be L. Then we can use the formula for the area of a rectangle:

Area = Length x Width

Substituting the given values, we get:

16 1/3 = L x 4 2/3

To solve for L, we can first convert the mixed numbers to improper fractions:

16 1/3 = 49/3

4 2/3 = 14/3

Substituting these values, we get:

49/3 = L x 14/3

To solve for L, we can multiply both sides by the reciprocal of 14/3:

49/3 ÷ 14/3 = L

Simplifying, we get:

L = 49/3 x 3/14

L = 7/1

L = 7

Therefore, the length of the rectangle is 7 inches.

Step-by-step explanation:

Answer:

Step-by-step explanation

90,000 is 20,853 greater than 69,147

Answer:

12 dollars

Step-by-step explanation:

480 / 40 = 12

12 dollars

Answer/Step-by-step explanation:

Angle 1 and angle 11 = none

No special relation between both angles.

Angle 1 and angle 6 = none

Both angles also do not have any special relationship

Angle 12 and angle 15 = same side interior

Angle 12 and angle 15 both interior angles that lie on the same side of the transversal that cuts across two straight lines. They are supplementary.

Answer:

75 grams

Step-by-step explanation:

If 25 cm = 10 grams

Then 1 cm = 25/10

1 cm = 2.5 grams

To find 30 cm = 2.5 times 30 grams

30 cm = 75 grams

To estimate the total distance traveled by the car in 36 seconds using a trapezium, we need to find the area under the curve of the graph. The trapezium can be constructed by connecting the points on the graph at the starting and ending times.

Let's break down the process into two parts:

Estimating the distance between 30 and 36 seconds:

To estimate the distance between 30 and 36 seconds, we can draw a triangle underneath that section of the curve. The base of the triangle is 6 seconds (36 - 30), and the height is the speed at 36 seconds (which is approximately 10 m/s). The area of the triangle is (base * height) / 2, so the estimated distance is (6 * 10) / 2 = 30 meters.

Estimating the distance using a trapezium:

To estimate the distance traveled in the first part of the graph (from 0 to 30 seconds), we can use a trapezium. The bases of the trapezium are the speeds at 0 and 30 seconds, which are approximately 25 m/s and 10 m/s, respectively. The height of the trapezium is the duration, which is 30 seconds. The area of the trapezium is ((base1 + base2) * height) / 2, so the estimated distance is ((25 + 10) * 30) / 2 = 525 meters.

Therefore, the estimated total distance traveled by the car in 36 seconds, using the trapezium and triangle approximation, is 30 meters + 525 meters = 555 meters.

Using mental maths to solve the problem of 8.02 - 5.98 gives a difference of 2.04.

Mental mathematics is the method of working out maths calculations and solving problems in one's head (mentally) without writing them down or using calculators.

Mental maths provides a quick way of arriving at arithmetical solutions without mathematical tools.

First value =       8.02

Second value = 5.98

Difference =      2.04

The mental method used to solve the problem is the removal of the decimal points, thus making the values look like these whole integers:

First value =       802

Second value = 598

Difference =      204

After obtaining the difference as 204, the two decimal places are replaced to arrive at the final answer.

Thus, using mental maths to solve the problem of 8.02 - 5.98 gives a difference of 2.04.

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Answer:

1+7(n-1)

Step-by-step explanation:

arithmetic formula

Answer:

x=7

(x)(x+1)=(4)(4+10)

Step-by-step explanation:

Expanding the right-hand side of the equation, we get:

(x)(x+1) = (4)(14)

Simplifying, we get:

x^2 + x = 56

Moving all terms to the left-hand side, we get:

x^2 + x - 56 = 0

Now we can factor this quadratic equation:

(x + 8)(x - 7) = 0

So the solutions are x = -8 or x = 7.

Answer: X=7

Step-by-step explanation:

To Solve this problem we have to remember a formula regarding secants in circles it states (A+B)*B=(C+D)*D, I have attached said Theorem. This is Exactly what your problem is asking.

So First

B = 4

A = 10

D = x

C = 1

(A+B)*B=(C+D)*D

(10+4)*4=(1+x)*x

14*4=x²+x

-x²-x+56=0

Using Quadratic Formula

X = 7, X = -8

Since you cant have - side length X= -8 is Extraneous

Thus Final solution is X = 7

Answer:

y = - x + 9

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, 9) and (x₂, y₂ ) = (9, 0) ← 2 points on the line

m = \(\frac{0-9}{9-0}\) = \(\frac{-9}{9}\) = - 1

the line crosses the y- axis at (0, 9 ) ⇒ c = 9

y = - x + 9 ← equation of line

Answer:

Angle 6 = 70

Step-by-step explanation: Using vertical angles if you look across from angle 6 you would see the angle of 70 degrees which means they are equal because they're across from each other.

To simplify the expression above, simply combine similar terms.

The similar terms in the expression above are 8c and -3c as well as 6 and -2.

Let's combine the pairs of similar terms.

So, 8c - 3c = 5c and 6 - 2 = 4. Hence, the answer is:

The answer is 5c + 4. (Option A)

Answer: (6,-6)

Step-by-step explanation:

To find the coordinates of point B, we can use the midpoint formula:

Midpoint formula: The midpoint M of a line segment with endpoints (x1, y1) and (x2, y2) is given by:

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

Here, we know that the midpoint M is (4, -2), and one endpoint A is (2, 2). Let B be the other endpoint, so we can use the midpoint formula to find B:

4 = (2+x2)/2 --> 8 = 2+x2 --> x2 = 6

-2 = (2+y2)/2 --> -4 = 2+y2 --> y2 = -6

Therefore, point B has coordinates (6, -6).

As for the second question, without a graph or information about the equation of line t and point P, it is not possible to determine which points lie on the line passing through P and perpendicular to t.

Answer:

Refer to the step-by-step explanation, please follow along very carefully. Answers are encased in two boxes.

Step-by-step explanation:

Given the following function, find it's derivative using the definition of derivatives. Evaluate the function when θ=1, 11, and 3/11

\(p(\theta)=\sqrt{11\theta}\)

\(\hrulefill\)

The definition of derivatives states that the derivative of a function at a specific point measures the rate of change of the function at that point. It is defined as the limit of the difference quotient as the change in the input variable approaches zero.

\(f'(x) = \lim_{{h \to 0}} \dfrac{{f(x+h) - f(x)}}{{h}}\)\(\hrulefill\)

To apply the definition of derivatives to this problem, follow these step-by-step instructions:

Step 1: Identify the function: Determine the function for which you want to find the derivative. In out case the function is denoted as p(θ).

\(p(\theta)=\sqrt{11\theta}\)

Step 2: Write the difference quotient: Using the definition of derivatives, write down the difference quotient. The general form of the difference quotient is (f(x+h) - f(x))/h, where "x" is the point at which you want to find the derivative, and "h" represents a small change in the input variable. In our case:

\(p'(\theta) = \lim_{{h \to 0}} \dfrac{{p(\theta+h) - p(\theta)}}{{h}}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11(\theta + h)} - \sqrt{11\theta} }{h}\)

Step 3: Take the limit:

We need to rationalize the numerator. Rewriting using radical rules.

\(p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11(\theta + h)} - \sqrt{11\theta} }{h} \\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11\theta + 11h} - \sqrt{11\theta} }{h}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} }{h}\)

Now multiply by the conjugate.

\(p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} }{h} \cdot \dfrac{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} } \\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{(\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} )(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )}{h(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )} \\\\\\\)

\(\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{11h}{h(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{11}{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }\)

Step 4: Simplify the expression: Evaluate the limit by substituting the value of h=0 into the difference quotient. Simplify the expression as much as possible.

\(p'(\theta)= \lim_{h \to 0} \dfrac{11}{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{\sqrt{11}\sqrt{\theta+(0)} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{\sqrt{11}\sqrt{\theta} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11\theta} }\)

\(\therefore \boxed{\boxed{p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta} }}}\)

Thus, we have found the derivative on the function using the definition.

It's important to note that in practice, finding derivatives using the definition can be a tedious process, especially for more complex functions. However, the definition lays the foundation for understanding the concept of derivatives and its applications. In practice, there are various rules and techniques, such as the power rule, product rule, and chain rule, that can be applied to find derivatives more efficiently.\(\hrulefill\)

Now evaluating the function at the given points.  

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}; \ p'(1)=??, \ p'(11)=??, \ p'(\frac{3}{11} )=??\)

When θ=1:

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(1)= \dfrac{\sqrt{11} }{2\sqrt{1}}\\\\\\\therefore \boxed{\boxed{p'(1)= \dfrac{\sqrt{11} }{2}}}\)

When θ=11:

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(11)= \dfrac{\sqrt{11} }{2\sqrt{11}}\\\\\\\therefore \boxed{\boxed{p'(11)= \dfrac{1}{2}}}\)

When θ=3/11:

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(\frac{3}{11} )= \dfrac{\sqrt{11} }{2\sqrt{\frac{3}{11} }}\\\\\\\therefore \boxed{\boxed{p'(\frac{3}{11} )= \dfrac{11\sqrt{3} }{6}}}\)

Thus, all parts are solved.

The expressions on the left matched with the simplified form on the right:

-(-9) = 9

|-9| = 9

-|9| = -9

|9| = 9

-|-9| = -9

Mathematical rules to simplify the expressions:

a negative sign multiplied by a negative sign is equal to a positive sign

a positive sign multiplied by a negative sign is equal to a negative sign.

a positive sign multiplied by a positive sign is equal to a positive sign.

Also, this sign | | indicates that the number is positive.

Therefore,

-(-9) = 9

|-9| = 9

-|9| = -9

|9| = 9

-|-9| = -9

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Answer: 519 120

Step-by-step explanation:

84*84=7056

7056/7=1008

1008*515=519 120

Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

Answer: Yes.

Step-by-step explanation:

If one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram. If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

       A) -  Event  "A  or  B"  Consists  of  the Outcomes:

               {2, 3, 4, 5, 6, 8}

      B) - Event  "A  or  "B"  Consists  of the Outcomes:

             {4,  6}

      C) -  The "COMPLEMENT  of EVENT  "A"  Consists of the Outcomes:

             {1, 3, 5, 7}

MAKE A PLAN:

List The OUTCOMES for EACH EVENT and their COMBINATIONS:

        a) -  EVENT  "A":  {2, 4, 6, 8}

               EVENT "B":   {3, 4, 5, 6}

               EVENT "A" or "B": {2, 3, 4, 5, 6, 8}

        b) - EVENT "A"  or "B":  {4, 6}

        c) -  The COMPLEMENT of the EVENT "A":  {1, 3, 5, 7}

       A) -  Event  "A  or  B"  Consists  of  the Outcomes:

               {2, 3, 4, 5, 6, 8}

      B) - Event  "A  or  "B"  Consists  of the Outcomes:

            {4,  6}

      C) - The "COMPLEMENT  of EVENT  "A"  Consists of the Outcomes:

             {1, 3, 5, 7}

I hope this helps!

Answer:

33/16 hope this helps

Step-by-step explanation:

The distance between the points where the points are given as \((5\frac 78, -\frac 12)\) and \((9\frac 34, -\frac 12)\) is 3.875 units

The points are given as

\((5\frac 78, -\frac 12)\) and \((9\frac 34, -\frac 12)\)

The distance between the points is calculated as

d  = √(x₁ - x₂)² + (y₁ - y₂)²

Where x and y are the coordinate points and d is the distance

Substitute the known values in the above equation

So, we have

\(d = \sqrt{(5\frac 78 - 9\frac 34)\² + (-1/2 + 1/2)\²\)

Evaluate the sum in the above equation

So, we have

\(d = \sqrt{(5\frac 78 - 9\frac 34)\²\)

Evaluate the exponents in the above equation

So, we have

\(d = (-5\frac 78 + 9\frac 34)\)

Evaluate the difference  in the above equation

So, we have

d  = 3.875

Hence, the distance between the points is 3.875 units

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Answer:

B. $48

Step-by-step explanation:

First we find the tip amount by multiplying the percent by the bill

20% * 40 = 8

We then add the tip amount to the bill

40 + 8

They payed a total of $48

The radius of the cylinder is 7. 9 in

First, we need to know the formula for volume of a cylinder

The formula for calculating the volume of a cylinder is expressed as;

V = πr²h

Such that the parameters of the formula are expressed as;

From the information given, we have that;

Substitute the values

196 = 3.14 × 1 × r²

Divide both sides by the values

r² = 62. 42

Find the square root of both sides

r = 7. 9 in

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The correct option that matches the graph is option A.

Graph is a fine representation of a network and it describes the relationship between lines and points. The length of the lines and position of the points don't count. Each object in a graph is called a knot.

The four introductory graphs used in statistics include bar, line, histogram and pie maps. The description of a graph is a illustration showing the connections between two or further effects. An illustration of graph is a pie map. noun. A wind or line showing a fine function or equation, generally drawn in a Cartesian match system.

Since it is upside down, it is the one with the negative sign in front of the x. The numbers will continue to increase in the negatives.

\(v=x^2-2x+1\)

Hence, the equation on option A matches the graph.

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Step-by-step explanation:

s1 = 5

s2 = s1 × -2 = 5×-2 = -10

s3 = s2 × -2 = -10 × -2 = 20

...

now, we could do all that manually.

but there is also a formula for geometric sequence.

in fact, there are 2 - one for finite and one for infinite sequences.

and I was not completely honest, each of these 2 had some sub-forms depending on the size of the multiplier or ratio.

since we need the sum of the first 5 terms, which of the 2 do you think we need ?

of course, finite, because 5 is a normal number we can "touch". it is not infinity.

so, the formulas for finite sums of geometric sequences are :

if |r| < 1, Sn = a(1 - r^n)/(1 - r)

if |r| > 1, Sn = a(r^n - 1)/(r - 1)

if r = 1, Sn = na

if r = -1, then Sn = a or 0 depending on if n is odd or even.

the sequence is in general

s1 = a

sn = sn-1 × r

in our case a = 5, r = -2.

so, what form of the formula do we need ?

|-2| = 2, and 2 > 1, so ...

S5 = 5(-2^5 ‐ 1)/(-2 - 1) = 5(-32 - 1)/-3 = 5×-33/-3 =

= 5 × 11 = 55

quick check, as the 5 terms are

5

-10

20

-40

80

and their sum is : 55

correct !

The correct option for the given sum is option B. The point (2,-9) paired with (2, 3), will make a side equal to this length.

Let the other point of the pentagon will be M(n, o).

The given point be A (a, b)

Also given one of the sides of a pentagon has length 12.

Now, we need to find the distance between the two points,

Distance between two points: |AM| = √\((a-n)^2+(b-o)^2\)

Now,

\(12 = \sqrt{(2-n)^2+(3-o)^2}\)

\((12)^2\) = \((2-n)^2+(3-o)^2\)

\((2-n)^2+(3-o)^2\) = 144 ----------------------------- eq (1)

Now, check every point for the values to match with equation (1)

Option A: \((2-14)^2+(3-15)^2\) = 288. So the option is false.

Option B:

\((2-2)^2+(3-(-9))^2\) =114

0+114 =114

Therefore option B is correct. The other point is (2,-9).

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\(\\ \sf\longmapsto UV=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

\(\\ \sf\longmapsto UV=\sqrt{(-5-2)^2+(-3+2)^2}\)

\(\\ \sf\longmapsto UV=\sqrt{(-7)^2+(-1)^2}\)

\(\\ \sf\longmapsto UV=\sqrt{49+1}\)

\(\\ \sf\longmapsto UV=50\)

Answer:

Option C is correct option.

Step-by-step explanation:

The option C : Yes it can, because-4.5 lies to the left of -3.5 is the correct option.

Reason:

-4.5 is less than -3.5 and it comes after -4 so it lies under the shaded region.

Option C is correct option.