Solve the following equation : 7x/15-1=22

Answer:

C)Reflected over the x-axis and rotated 90 degrees counterclockwise

Step-by-step explanation:

Reflection over the x-axis move point C from (-1, 1) to (-1, -1), point D from (-1, 2) to (-1, -2), point A from (-4, 2) to (-4, -2) and point B from (-4, 1) to (-4, -1). As can be seen, y-coordinate changes sign, so that, the distance between the original point and its reflection respect x-axis remains the same.

Rotation 90 degrees counterclockwise around origin means that x-coordinate and y-coordinate switches and x-coordinate is multiplied by -1. So, point (-1, -1) transforms into (1, -1) - point C' -, (-1, -2) transforms into (2, -1) - point D' -, point (-4, -2) transforms into (2, -4) - point A' - and point (-4, -1) transforms into (1, -4) - point B'.

Answer:

[tex](-2,0)[/tex] and [tex](3,5)[/tex]

Step-by-step explanation:

we have

[tex]y+4=x^{2}[/tex] -----> equation A

Is a vertical parabola open upward

[tex]y-x=2[/tex] ----> equation B

Is the equation of a line

we know that

The solution of the system of equations is the intersection point both graphs

Using a graphing tool

The intersection points are [tex](-2,0)[/tex] and [tex](3,5)[/tex]

see the attached figure

9,    12,    19,    30,    ...

Answer with explanation:

⇒Arithmetic Sequence

    11,21,31,41,51,......

First term[tex]a_{1}[/tex] =11

Common Difference(d)=21-11=10

  [tex]\rightarrow a_{n}=a_{n-1}+10---{\text{Recursive formula}}\\\\\rightarrow a_{n}=a_{1}+(n-1)d\\\\a_{n}=11+(n-1)\times 10\\\\a_{n}=10n+1---{\text{Explicit formula}[/tex]

⇒Geometric Sequence

 First five terms of the sequence are

[tex]4,4^2,4^3,4^4,4^5,.....\\\\\text{First term}=a_{1}=4\\\\ \text{Common ratio},r=\frac{a_{2}}{a_{1}}\\\\r=\frac{4^2}{4}\\\\r=4\\\\a_{n}=4\times a_{n-1}---\text{Recursive formula}\\\\a_{n}=a_{1}\times r^{n-1}\\\\a_{n}=4\times 4^{n-1}\\\\a_{n}=4^{1+n-1}\\\\a^n=4^n-----\text{Explicit formula}[/tex]

Answer:

AC = 21⁰

Step-by-step explanation:

arc AC has central angle 3x+9 n its inscribed angle <ABC is 3x-1.5

central angle = 2 * inscribed angle

3x+9 = 2 * (3x-1.5)

3x+9 = 6x -3

3x = 12

x = 4

so arc AC = (3*4 + 9) = 21⁰

The expression which shows the change in Carlotta's savings is x-8 if her she owes her brother $6.

An expression is a combination of numbers, symbols and variables but not in equal to form.

In the problem Jasmine and Carlotta borrowed $28 from their brother. Since both need to pay back equally so Carlotta needs to pay back $14 but she owes 6 from her brother so she now  has to pay only 8.

Let the savings be x

in this way only $8 needs to be subtracted from savings.

The expression will be = x-8.

Hence the expression which shows the change in savings is x-8.

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Exponents multiply a number by itself, while exponential functions contain variables in the exponent. Algebra 1B tasks involving these could include simplifying exponents, solving problems with exponential functions, and creating or interpreting an Exponential Functions Table. Studying, understanding rules, and practicing problems will aid success.

It seems like you need help with understanding Exponents and Exponential Functions. Exponents are a way of multiplying a number by itself. For example, 2^3 means 2 is multiplied by itself twice (2 * 2 * 2).

On the other hand, exponential functions are a special type of functions where the variable is in the exponent. For instance, the function f(x) = 2^x is an exponential function.

For your Algebra 1B tasks, here's a sample process: for Task 1, you might be required to simplify numbers or expressions using exponents. Task 2 may require you to solve problems using exponential functions. And Task 3 could involve creating or interpreting an Exponential Functions Table, which is a table showing the values of an exponential function for different x-values.

Remember to follow your study guides, textbooks, and your teacher's instructions for each task. Practicing problems and understanding the rules of exponents and exponential functions will help you earn those 30 points!

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By definition, the surface area of a sphere is given by:

[tex] A = 4 * \pi * r ^ 2
[/tex]

Where,

r: sphere radius

Substituting values in the given equation we have:

[tex] A = 4 * 3.14 * 8 ^ 2
[/tex]

Doing the calculations we have:

[tex] A = 803.84
[/tex]

Rounding to the nearest tenth:

[tex] A = 803.8 cm ^ 2
[/tex]

Answer:

The surface area of a sphere with a radius of 8cm is:

B. 803.8 cm ^ 2

A graph that correctly represents the exponential function [tex]f(x) = 2^x[/tex] include the following; B. graph B.

In Mathematics and Euclidean Geometry, an exponential function can be modeled by using this mathematical equation:

[tex]f(x)=a(b)^x[/tex]

Where:

Based on the information provided above, we would select the following exponential function to plot on a set of axes or cartesian coordinate;

[tex]f(x) = 2^x[/tex]

where:

The rate of change (b) is 2 and it represents an exponential growth.

The y-intercept (a) is 1 and it means the graph of this function would cross the y-axis at point (0, 1).

In conclusion, we can logically deduce that only graph B correctly represent an exponential function with these key features.

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Missing information:

Which of the following graphs represents the function [tex]f(x) = 2^x[/tex]?

Karen's situation can be modeled by the following system of inequalities:

Total number of utensils: p + n ≤ 25 (p = number of pens, n = number of pencils)

Pencils vs. pens: n ≥ (3 - p)^2 (pencils must be at least the square of 3 less than the number of pens)

Viable solutions: All solutions within this system are viable.

First inequality: This ensures that the total number of writing utensils (pens + pencils) doesn't exceed 25, Karen's desired maximum.

Second inequality: This accounts for Karen's preference for having at least as many pencils as the square of 3 less than the number of pens. It avoids solutions with fewer pencils than the squared difference.

Viable solutions: Since both inequalities are valid and independent, any solution that satisfies both is acceptable. This leaves a broad range of viable combinations of pens and pencils, allowing Karen flexibility within her limits.

Therefore, all solutions within the system of inequalities are valid possibilities for Karen's purchase. She can choose any combination of pens and pencils as long as their total is 25 or less and the number of pencils is greater than or equal to the square of 3 less than the number of pens.

Answer:

6ft.

Step-by-step explanation:

The amount that Colin will get more than Paul is $7.90.

From the information given, Paul's share will be:

= 2/9 × $71.10

= $15.80

The share of Colin will be:

= 3/9 × $71.10

= $23.70

The difference between Colin's share and Paul's share will be:

= $23.70 - $15.80

= $7.90

Therefore, the amount that Colin will get more than Paul is $7.90.

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An equation of the line in slope-intercept form that passes through the point (-9, 17) and has a slope of -4/3 is y = -4x/3 + 5.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

At data point (-9, 17) and a slope of -4/3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 17 = -4/3(x - (-9))

y - 17 = -4x/3 - 12

y = -4x/3 - 12 + 17

y = -4x/3 + 5

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Complete Question:

Write an equation in slope-intercept form of the line that passes through the point (-9,17) and had a slope of -4/3.

Answer with explanation:

If the length of three segments are, 9.2, 14.5 and 17.1 ,it can be sides of triangle if , Sum of two segments is greater than the third segment.

1.→ 9.2 +14.5=23.7 >17.1

2.→ 14.5 +17.1=41.6 > 9.2

3.→17.1 +9.2=26.3 >14.5

As, sum of any two segment is greater than third segment, so the following measurements can be the the lengths of the sides of a triangle.