Mathematics High School

## Answers

**Answer 1**

The **perimeter** of the possible **larger triangle** with possible side lengths of 24, 32 and 40 is 96 units

What is the perimeter of a plane figure?

The **perimeter** of a figure is the **length** of the boundary **surrounding** the figure.

**Two triangles** that have **proportional** dimensions are similar triangles

The **dimensions** (arranged in the order of **corresponding** sides) of the possible **similar right triangles** in the question, obtained from a related question, having two similar right triangles, posted online are;

First (larger) triangle side lengths; 24, 32, and *x*Second (smaller) triangle side lengths; 9, 12, and 15

The similarity of the triangles (proportional corresponding sides, indicates that we get;

[tex]\dfrac{24}{9} = \dfrac{32}{12} = \dfrac{x}{15}[/tex]

Therefore, by cross multiplication, we get;

32 × 15 = 12 × x

x = 32 × 15 ÷ 12 = 40

The **perimeter** of the larger triangle is; 24 + 32 + 40 = 96

The perimeter of the larger triangle is 96 units.

Please find attached the possible diagram of proportional right triangles, created with MS Word, obtained from a question with regards to proportional right triangles online.

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## Related Questions

2 The test statistic in a two-tailed test is z=-2. 75 use a 0. 05 significance level to find the P value and state the conclusion about the null hypothesis

### Answers

The p-value of the test statistic is p-value = 0.006. The **null hypothesis** will be rejected at 5% level of significance.

What Is Two-Tailed Test?

A two-tailed test in **statistics** determines if a sample is more than or less than a **specific range** of values by using a two-sided critical area of a distribution. It is employed in testing the null hypothesis and determining **statistical significance**. The alternative hypothesis is accepted in place of the null hypothesis if either of the critical areas apply to the sample under test.

A two-tailed test in statistics determines if a sample is greater or less than a range of values by using a two-sided critical area of a distribution.

It is employed in testing the null hypothesis and determining statistical significance.

The alternative hypothesis is accepted in place of the null hypothesis if either of the crucial areas apply to the sample under test.

Conventionally, two-tailed tests with a 2.5% cutoff on each side of the distribution are employed to evaluate significance at the 5% level.

How to calculate the p-value?

Determine the level of relevance, sometimes referred to as the level, in step one. Assume 0.05 if it isn't specified. Step 2: Evaluate the level of significance in relation to the p-value. Make the conclusion that supports the possible change and reject the null hypothesis if the p-value is lower.

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Find the centre focus,vertex,directrix and axis of each parabola and sketch the graph? (x-1)² = y+2

### Answers

The **answers** to each part of the question are mentioned above.

What is parabola?In mathematics, a parabola is a plane curve which is **mirror-symmetrical** and is approximately U-shaped.The general equation of a **parabola** is given by -

y = a(x – h)² + k or x = a(y – k)² +h.

where -** (h, k)** denotes the vertex.

Given is the equation of a **parabola** as -

(x - 1)² = y + 2

We can write the equation as -

y = (x - 1)² - 2

The coordinates of the **vertex** are : (h, k). So, we can write the coordinates of the vertex as **V(1, - 2)**.The equation of a parabola is -

[tex]$y=\frac{1}{4 \left(f - k\right)} \left(x - h\right)^{2} + k[/tex]

We can rewrite the equation of the parabola given as -

[tex]$y=\frac{1}{4 \left(\frac{-7}{4} - (-2)\right)} \left(x - h\right)^{2} + k[/tex]

The coordinates of the** focus** are : (h, f). The coordinates of the focus will be - F(h, f) or **F(1, -7/4)**The distance from the focus to the vertex is the **same** as the distance from the vertex to the directrix so -

- 2 - (- 7/4) = d - (- 2)

d = - 9/4

The equation of directrix will be :

y = d

** y = -9/4 **

The **axis of symmetry** is the line perpendicular to the directrix that passes through the vertex and the focus: **x = 1**

Therefore, the **answers** to each part of the question are mentioned above.

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PLEASE HELP ME I DONT UNDERSTAND

Question 1: The Magnolia trees purchased for planting at the school are 3 feet tall. Research shows that these types of trees grow at an average of 3/4 foot per year Some students misunderstood question #1 and wrote the following equations in point-slope form:

a) y − 3 = 3/4(x-0)

b) y - 6 = 3/4(x-4)

c) y - 4.5 = 3/4(x-2)

d) y - 12 = 3/4(x-12)

e) y - 15= 3/4(x-15)

Is point slope form okay to use to find the height of the trees in this problem?

There is one equation that is incorrect.... determine which one? why is it incorrect?

Creat two new equations written in point slope form

### Answers

The **point slope **form is not okay to use to find the **height** of the trees

The **incorrect **equation is y - 15= 3/4(x-15) The other **equations **are y - 3.75 = 3/4(x - 1) and y - 4.5 = 3/4(x - 2)

How to determine if the point slope form is okay?

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

**Initial height **of purchase = 3 feet tallAverage **rate **= 3/4 foot per year

The **point slope form **of a linear equation is represented as

y - y₁ = m(x - x₁)

Where

Slope = m

The **point slope form **does not show the initial value

So, this form is not okay for the required parameters

How to determine the incorrect equation

The slope-intercept form is given as

y = mx + c

Using the given parameters, we have

y = 3/4x + 3

Subtract 3 from both sides

y - 3 = 3/4x

Rewrite as

y - 3 = 3/4(x - 0)

This **equation **can be rewritten in any of the following forms

a) y − 3 = 3/4(x-0)b) y - 6 = 3/4(x-4)c) y - 4.5 = 3/4(x-2)d) y - 12 = 3/4(x-12)

Hence, the incorrect equation is y - 15= 3/4(x-15)

Two new equations written in point slope form

We have the slope-intercept form to be

y = 3/4x + 3

Set x = 1 and 2, and then solve for y

So, we have

y = 3/4 * 1 + 3 = 3.75

y = 3/4 * 2 + 3 = 4.5

So, the equivalent equations are

y - 3.75 = 3/4(x - 1) and y - 4.5 = 3/4(x - 2)

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5.

4.2 cm

4.2 cm

square centimeters

### Answers

The **total area** of triangle in square centimeters is 56.7cm squared .The three angles of the triangle add up to 180 degrees.

what is triangle ?

The term "trigon" is occasionally (though not frequently) used to refer to a triangle, a 3-sided polygon. Every triangle consists of a set of three **angles** and three sides, some of which may be the same. The three angles of the triangle add up to 180 degrees. With three sides and three vertices, triangles are a specific type of polygon in **geometry**. The two-dimensional figure displayed here has three straight sides. A triangle is a type of 3-sided polygon.

here

Area of each triangles is 4.2 x 8.2 or 34.44.

There are two triangles, thus you don't need to divide by two.

In addition, 8.2 is obtained by deducting the top length from the overall length. (13.5-5.3)

rectangle: 22.26 x 5.3

56.7 square meters is the entire area.

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The correct question is

What is the area, in square centimeters, of the triangles are?

a) 5.3 cm

b) 4.2 cm

c) 13.5 cm

4 Siobhan and Ralph shared £700 in the

ratio 2:3.

Siobhan gave a quarter of her share to Karen.

Ralph gave a fifth of his share to Karen.

What fraction of the £700 did Karen receive?

### Answers

Therefore ,the solution to the given problem of** proportion** comes out to be karen got £70.

What is a proportion?

The rule of three is used to link the measures because a proportion is a fraction of a total amount. It is possible to construct **equation **or relations between **variables** that are either direct (when both rise or decrease) or inverse proportional (when one increases and the other declines, or vice versa) in order to determine the necessary measures in the situation.

Here,

Given :

Siobhan and Ralph shared £700 in the

ratio 2:3.

Thus,

280 / 420 = 2/3

Thus,

Siobhan and Ralph has £280 and £420 respectively.

and Siobhan gave a share of quarter to karen :

So,

280/4 =70

Therefore ,the solution to the given problem of proportion comes out to be karen got £70.

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What is the log value of log2?

### Answers

The log value of log2 is 1Log2 is defined as the logarithm base 2. This means that the **logarithm of any number x** is equal to the power to which the base 2 must be raised to** produce x. **

In other words, log2(x) = y, where 2^y = x.

Therefore, when x = 2, 2^y = 2. This means that the logarithm of 2 is equal to 1, since 2^1 = 2.

Therefore, the log value of log2 is 1.

Log2 is an important mathematical concept that is used to calculate the logarithm of a number. Logarithms are used in a variety of fields, including mathematics, physics, engineering, and computer science. Log2 is the **logarithm** with a base of 2, which means that the logarithm of any number x is equal to the **power** to which the base 2 must be raised to produce x. To calculate log2 of a number, the formula is log2(x) = y, where 2^y = x. This means that the logarithm of 2 is equal to 1, since 2^1 = 2. Therefore, the log value of log2 is 1. Log2 is often used to calculate logarithms of **numbers** that are not powers of 2, such as log2(3) = 1.5849. Log2 can also be used to calculate logarithms of numbers with decimals, such as log2(1.5) = 0.5849. Log2 can also be used to calculate **exponents**, such as 2^3 = 8.

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What is the difference of the two polynomials 9x2 8x 2x2 3x?

### Answers

The **difference **between the **polynomials **9x² + 8x and 2x² + 3x is 7x² + 5x.

What is **polynomials**?

A **polynomial **is formed mathematically by combining one or more **algebraic terms **(**monomials**). The roots of "**polynomial**" are poly- (many) and -nomial (**terms**). A **polynomial **can have exponents (powers), constants (numbers), and variables (letters), but not negative exponents or variable division.

**Polynomials **are typically expressed in standard form. Furthermore, because there are no similar **terms **among the **exponents**, they are arranged in descending order (largest to smallest).

To find the **difference **between

(9x² + 8x) - (2x² + 3x)

We do calculation

= 9x² + 8x - 2x² - 3x

= 9x² - 2x² + 8x - 3x

= 7x² + 5x

Thus, the **difference **between the **polynomials **is 7x² + 5x.

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A 5 m 60 cm high vertical pole cat a hadow 3 m 20 cm long. Find at the ame time

(i) the length of the hadow cat by another pole 10 m 50 cm high,

### Answers

On solving the provided question we can say that **equation **formed is x/y = k, x = ky => y₂ = (10.5 × 3.2) / 5.6 => y₂ = 6

What is equation?

An equation is a **mathematical formula **that connects two assertions using the **equal sign **(=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

x/y = k, x = ky

where k is a constant.

Thus, x₁ / y₁ = x₂ / y₂

5.6 / 3.2 = 10.5 / y₂

5.6 × y₂ = 10.5 × 3.2

y₂ = (10.5 × 3.2) / 5.6

y₂ = 6

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You know that 4 movie tickets in Virginia plus 5 movie tickets in Maryland cost $77. You also know that 8 movie tickets in Virginia plus 3 movie tickets in Maryland cost $91. How much does a ticket in Virginia cost?

### Answers

The cost of one ticket in **Virginia **is $8

What is a **system of linear equations?**

A System of Linear **Equations **is when we have two or more linear equations working together.

Given that, 4 movie tickets in **Virginia **plus 5 movie tickets in **Maryland **cost $77, Also know that 8 movie tickets in **Virginia **plus 3 movie tickets in **Maryland **cost $91.

To find the cost of a ticket in **Virginia** we will establish a **system of linear equations **and then solve them,

Let V represents the cost in **Virginia **that of in **Maryland **be M

Therefore,

4v+5m = 77.......(i)

8v+3m = 91........(ii)

Multiplying the **equation **eq(i) by 2 and **subtracting **eq(ii) from eq(i) [Elimination]

(8v+10m = 154) - (8v+3m = 91)

7m = 63

m = 9

Put m = 9 in eq(i)

4v+5(9) = 77

4v = 77-45

4v = 32

v = 8

Hence, Each ticket in **Virginia **and **Maryland **costs $8 and $9 respectively.

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Tara placed the numbers -2 1/6, 3/11 and 2 2/9 on the number line below. Which letters

represent the correct location for each number?

-2 1/6 is A, 3/11 is C, and 2 2/9 is E

or

-2 1/6 is A, 3/11 is D, and 2 2/9 is E

or

-2 1/6 is A, 3/11 is D, and 2 2/9 is F

or

-2 1/6 is B, 3/11 is D, and 2 2/9 is F

### Answers

**Answer:**

sorry beacuse I don't know anything

Could someone please help me?

### Answers

[tex]\textit{area of the rectangle}\\\\ A=Lw \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ L=5\\ w=6 \end{cases}\implies A=(5)(6)\qquad \begin{cases} \textit{tripling the sides}\\[-0.5em] \hrulefill\\ L=3\cdot 5\\ w=3\cdot 6 \end{cases} \\\\\\ A=(3\cdot 5)(3\cdot 6)\implies (3\cdot 3)(5)(6)\implies 9(5)(6)\leftarrow \begin{array}{llll} \textit{new area is 9 times}\\ \textit{the old one}\\ \textit{a ratio of 9 : 1} \end{array}[/tex]

URGENT!! 25 POINTS!!!!!

What is the equation shown

by the following graph?

### Answers

**Answer:**

denominator - 6234 is math

**Step-by-step explanation:**

a smallercircle passes through the center of, and is tanget to a larger cirlc the area of the smaller circle is 9 square units. What is teh area of the larger circle in square units

### Answers

36 square units make up the larger **circle's surface area**.

We can use the fact that the** smaller** circle is **tangent** to the larger circle and passes through its** center** to find the** area** of the larger circle. Since the **radius** of the smaller circle is** tangent** to the larger circle, the radius of the larger circle is** double** the **radius** of the smaller circle.

Let's call the** radius** of the smaller circle "r" and the radius of the** larger **circle "R". We know that R = 2r.

We know that the **area** of a circle is given by the **formula **A = πr^2.

We know that the **area **of the smaller circle is 9 square units, we can use this formula to find the radius:

A = πr^2 => r^2 = 9/π => r = sqrt(9/π)

Now we can use the formula of the **area** of a** circle** with R-value to get the area of the **larger **circle:

A = πR^2 => A = π(2r)^2 => A = 4πr^2 => A = 4π(9/π) => A = 36

So the** area** of the larger circle is 36 square units

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A mountain on a tropical island experiences changes in its height due to volcanic activity. Its current height is 2,827 meters, which is 10% taller than it was when the mountain was last measured. How tall was it then?

### Answers

**Answer:**

2,570 meters

**Step-by-step explanation:**

110% of what number is 2827

1.1x = 2827 Divide both sides by 1.1

[tex]\frac{1.1x}{1.1}[/tex] = [tex]\frac{2827}{1.1}[/tex]

x = 2570

True or false? The graph represents a function.

### Answers

Answer:

true :)

Step-by-step explanation:

answer is true ! graph shows a function

a pair of sneakers in on sale as shown the sale price is $51. This is 75% of the original price. what was the original price of the shoes

pls help, explanation required

### Answers

$204

If you take 1- .75= .25 then you take 51 divide by .25 then you get the original price of 204. To check you answer you can take 204 x .75=153 then you take 204-153=51

Jeremiah completed a straight, 120 km drive in 1.5 hours. At one point during the drive, he saw that his speedometer read 105 km/h. Which of the following statements are accurate?

His average velocity was 105 km/h.

His instantaneous velocity was always 105 km/h.

His instantaneous velocity was always 80 km/h.

At one point, his instantaneous velocity was 105 km/h.

His average velocity was 80 km/h.

### Answers

Jeremiah** average velocity **during the drive was 80 km/h while the **instantaneous velocity** at one point was 105 km/h

What is an **equation**?

An equation is used to show the **relationship** between numbers and variables.

Average velocity is the **ratio **of** total distance** travelled to **total time** taken. Instantaneous velocity is the velocity at a** particular point** in time.

Jeremiah completed a straight, 120 km drive in 1.5 hours, hence:

Average velocity = total distance / total time

Average velocity = 120 km / 1.5 hours = 80 km/h

At one point during the drive, he saw that his speedometer read 105 km/h, hence:

Instantaneous velocity = 105 km/h

The** average velocity **is 80 km/h while the **instantaneous velocity** is 105 km/h

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Right triangle $ABC$ has one leg of length 6 cm, one leg of length 8 cm and a right angle at $A$. A square has one side on the hypotenuse of triangle $ABC$ and a vertex on each of the two legs of triangle $ABC$. What is the length of one side of the square, in cm

### Answers

One side of the **square** has a length of 10 cm.

The** triangle** $ABC$ is a **right** triangle and it has one leg of length 6 cm and one **leg **of length 8 cm. Using the **Pythagorean **theorem, we can find the length of the **hypotenuse**:

c^2 = a^2 + b^2

c = √(a^2 + b^2)

c = √(6^2 + 8^2)

c = √(36 + 64)

c = √(100)

c = 10

So the** hypotenuse** of **triangle** $ABC$ has a length of 10 cm.

The **square** has one side on the **hypotenuse **of the triangle $ABC$ and a **vertex** on each of the two legs of the triangle $ABC$. Since the **square** is on the **hypotenuse** of the triangle, one side of the **square** has the same length as the** hypotenuse** of the triangle, which is 10 cm.

Therefore, one side of the **square** has a length of 10 cm.

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A frictionless pendulum is pulled 3 feet to one side of its center resting point…

### Answers

**A.** The amplitude of the **sinusoidal **function 's' would increase.

**B.** The midline of the sinusoidal curve will upshift.

What is a periodic function?

A function that repeats its values at **regular intervals **is said to be periodic. For instance, periodic functions include trigonometric functions, which repeat every 2 pi radian. In science, periodic functions are used to describe oscillations, waves, and other periodic events. Aperiodic refers to any nonperiodic function.

We know the moving mechanism of the pendulum can be graphed as a **periodic **function.

**A.** If the pendulum is pulled farther away from its resting point it will reach a greater height on both sides this would have an effect of an increase in the **amplitude **of the sinusoidal curve.

**B. ** If the pendulum is pulled farther away from its resting point the midline of the sinusoidal curve would **move up **along the y direction as a result of an increase in magnitude.

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A container has 2 cups of milk in it. How many 1/4 cups are in the container?

Explain or show your reasoning.

### Answers

the answer is 8. to find this answer you can divide 2 by 1/4…multiply the 2 by the reciprocal of 1/4. 2 * 4/1

the current ratio of Sara's sales to Ravi's sales is 100:2 would you earn a greater total commission with Sara or Ravi?

as a professional artist assume you will make pieces of art that sell at the same sales ratio as the artist with whom you apprenticed. would you earn more as a professional after apprenticed for Sara or Ravi?

### Answers

One would earn more if one apprenticed for Sara as a professional artist as evident judging from the current **sales ratio** and **commission rates.**

Which of Sara and Ravi guarantees more earnings after apprenticeship?

As evident in the task content; the current **ratio** of Sara's sales to Ravi's sale is 100 : 2.

Since Sara's pieces of art sell for $25, the total earnings is; 25 × 100 = $2500.

Hence, since the commission rate is 60%, it follows that the commission **earned** on sales of Sara's pieces is; 60% of 2500 = 0.6 × 2500 = $1500.

Also, since Ravi's pieces each cost $2000, it follows that for 2 pieces, the total earnings is; 2 × $2000 = $4,000.

Hence, since the **commission rate** for Ravi's pieces is 25%, the commission earned is therefore; 25% of 4000 = 0.25 × 4000 = $1000.

Ultimately, one would earn more if one apprenticed for Sara.

Complete question; Sara's pieces of art sell for $25 each your commission is 60%.

Ravi's pieces of art sell for $2000 each and your commission is 25%.

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explanation with steps

### Answers

**Answer:**

x = 40° , y = 140° z = 10°

**Step-by-step explanation:**

the sum of the 3 angles in a triangle is 180° , then

x + 60° + 80° = 180°

x + 140° = 180° ( subtract 140° from both sides )

x = 40°

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

y is an exterior angle of the triangle , then

y = 60° + 80° = 140°

x is also an exterior angle , then

30° + z = x

30° + z = 40° ( subtract 30° from both sides )

z = 10°

Use the graph of the function to find the domain and range of f. (Enter your answer using interval notation.)

### Answers

The **domain** and **range** of the functions are Domain: (-∞,∞),{x|x∈R} and Range: [4,∞),{y|y≥4}.

What is vertex form of a quadratic function of graph?

The **vertex form** of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola. The coefficient a determines whether the graph of a quadratic function will open upwards or downwards.

From the graph, **vertex** is (h, k)=(0, 4) and (x, y)=(2, 0)

Here, y= a(x - h)² + k

0=a(2-0)+4

-4=2a

a=2

Substitute, a=2 and (h, k)=(0, 4) in y= a(x - h)² + k, we get

y=2(x-0)²+4

y=2x²+4

So, f(x)=2x²+4

Find the **domain** by finding where the function is defined. The range is the set of values that correspond with the domain.

Domain: (-∞,∞),{x|x∈R}

Range: [4,∞),{y|y≥4}

Now,

(a) f(-3)= 2(-3)²+4=18

(b) f(2)= 2(2)²+4=12

(c) f(0)= 2(0)²+4=4

(d) f(3)= 2(3)²+4=18

Therefore, the **domain** and **range** of the functions are Domain: (-∞,∞),{x|x∈R} and Range: [4,∞),{y|y≥4}.

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NEED HELP QUICKLY!

x=?

y=?

### Answers

9x +12 +3x =180 (because of f angles since they are corresponding)

12x + 12 = 180

12x = 180 - 12

12x = 168

X = 168/12

X = 14

4y -10 + 3x = 180

4y -10 + 3(14) = 180

4y -10 +42 = 180

4y +32=180

4y = 180-32

4y= 148

Y = 148/4

Y = 37

What is the image of ( 12 , − 4 ) (12,−4) after a dilation by a scale factor of 1 4 4 1 centered at the origin?

### Answers

What is the **image **of ( 12 , − 4 ) after a **dilation** by a scale factor of 1/4 centered at the o**rigin** is (3, -1)

What is **transformation**?

Transformation is the **movement** of a point in the** coordinate plane**. Types of transformation are rotation, reflection, translation and dilation.

Dilation is the** increase or decrease** of a figure by a** scale factor** k. If the value of k > 1, then it is an enlargement but if k < 1, it is a reduction.

The point (12, -4) is dilated by a **scale factor **of 1/4 using the rule (x, y) ⇒ (x/4, y/4). The new point is (4, -1)

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What is the x-intercept of the graph of y x2 4x 4?

### Answers

The x-intercept of the **graph **of y = x² - 4x + 4 is x = 2.

By looking at the **equation**, we may determine the y-intercept when the equation is expressed in the slope-intercept form (y=mx+b). The y-**intercept** is the value of b. This is due to the fact that the y-intercept occurs when the x value is 0. Y = B when x = 0, since mx = 0 at this point.

We set y = 0 and solve the **equation **for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by **substituting **0 where necessary and then solving for the final variable.

The **formula **for the x-intercept is y = 0: The x-intercept(s) can be determined by factoring or by employing the **quadratic **formula because ax2 + bx + c=0.

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What i the invere of f(x) = 3/(x 1) f ^ - 1 * (x) = (3 - 1)/x f ^ - 1 * (x) = 3 x f ^ - 1 * (x) = x^ 1 2 f ^ - 1 * (z) = 3/x - 1

### Answers

The** inverse** of f(x) = 3/(x-1) is f^-1(x) = 3/x - 1.

So the correct answer is f ^ - 1 * (x) = 3/x - 1

The **inverse** of a function, denoted f^-1(x), is a function that "undoes" the original function. To find the inverse of a function, we need to switch the roles of x and y and then solve for x.

Given the **function** f(x) = 3/(x + 1), we can find its inverse by:

y = 3/ (x + 1)

Multiply with (x + 1) and divide by y

y(x + 1)/ y = (3/ (x + 1))×(x + 1)/ y

x + 1 = 3/ y

x = 3/ y - 1

Switching the roles of x and y:

y = 3/ x - 1

Thus **f^(-1)(x)** = 3/ x - 1

It's worth noting that in order for a function to have an inverse function it must be a **one-to-one** function. This means that for every y value there is only one x value.

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Liam Brought 5/8 Pound of cherries. Harrison Brought more cherries than Liam. Which could be the amountOf cherries that Harrison brought ?

### Answers

The **amount **of cherries bought by the Harrison is 62.5 pounds.

A **fraction **is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.

The amount of cherries bought by the Harrison should be more than the cherries bought by the Liam which is 5/8. Thus, The amount of cherries bought by the Harrison is **more **than the 5/8 or 62.5 pounds of cherries percent.

The cherries bought by the Liam is 5/8 pounds

The cherries bought by the Harrison is more than the Liam.

As in the problem the number of cherries bought Harrison (let) should be more than the cherries bought by the Liam (let ). Therefore,

H > L

As we know that the number of cherries bought by the Liam is 5/8 pounds. Keep the value of in the above equation, we get,

H > 5/8

This equation can be rewritten in the percentile form as,

h > (5/8) * 100 %

h > (5/2) * 25 %

h > 62.5 %

Hence, The **amount **of cherries bought by the Harrison is more than 5/8 pounds or 62.5 pounds of cherries percent.

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Pls help

(3 x 8 x 5)⁷

### Answers

To evaluate (3 x 8 x 5)⁷, you need to first **multiply **3, 8, and 5 together to get the **base**, then raise that result to the seventh **power**.

**What does a math exponent mean?**

The number of times a number has been multiplied by itself is referred to as an **exponent**. For instance, the expression 2 to the third (written as 23) signifies 2 x 2 x 2 = 8. 23 and 2 x 3 = 6 are not equivalent. Keep in mind that any number is itself when raised to the **power** of 1.

So,

(3 x 8 x 5)⁷ = (120)⁷ = 120 x 120 x 120 x 120 x 120 x 120 x 120

= (1.2 x 10^2)^7 = 1.2 x 10^2 x 1.2 x 10^2 x 1.2 x 10^2 x 1.2 x 10^2 x 1.2 x 10^2 x 1.2 x 10^2

=1.2^7 x 10^14 = 1.2^7 x 10^14

=4096 x 10^14

=4.096 x 10^17

Therefore (3 x 8 x 5)⁷ = 4.096 x 10^17

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A rectangular school banner has a length of 21 inches and a perimeter of 66 inches. A sign is made that is similar to the school banner and has a length of 7 inches. What is the perimeter of the sign?

### Answers

The **perimeter **of the sign is 22 inches.

**What is mean by Rectangle?**

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

A rectangular **school banner** has a length of 21 inches and a perimeter of 66 inches.

Let the perimeter of the sign for the **length **of 7 inches of the banner = x

So, By definition of **proportion**, we get;

⇒ 21 / 66 = 7 / x

Solve for x;

⇒ x = 7 × 66 / 21

⇒ x = 22

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