Mathematics High School

## Answers

**Answer 1**

Some **solutions **for the given** linear inequality:**

y < 0.5x + 2

are:

{(0, 1), (1, 2), (2, 2)}

Which points are solutions of the linear inequality?

Here we have the** linear inequality:**

y < 0.5x + 2

To find the points we can **evaluate **the right side, and then find values of y such that the **inequality **is true.

For example, if we use x = 0, then we get:

y < 0.5*0 + 2

y < 2

A value of y such that this is true is y = 1

Then the point (0, 1) is a **solution **of the **inequality**.

Another example can be with x = 1:

y < 0.5*1 + 2

y < 2.5

This time we can select y = 2, then the **solution **is (1, 2).

To get a final solution we can **evaluate **in x = 2

y < 0.5*2 + 2

y < 3

Then a possible solution is y = 2 again, so the **solution **is (2, 2).

Notice that for each of these values of x, there are a lot of other points that are **solutions**.

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## Related Questions

Which expression is a perfect cube?

-8x^21y^8

-64x^64y^64

-125x^9y^20

-216x^9y^18

### Answers

**Answer:**

[tex]-216x^9y^{18}[/tex]

**Step-by-step explanation:**

[tex]~~-216 x^9 y^{18}\\\\=(-6)^3 (x^3)^3 (y^6)^3\\\\=(-6x^3 y^6)^3[/tex]

Plot A shows the number of hours ten girls watched television over a one-week period. Plot B shows the number of hours ten boys watched television over the same period of timeWhich statement correctly compares the measures of center in the two sets of data? Both the mean and median are greater for Plot A than for Plot B. Both the mean and median are greater for Plot B than for Plot A. Plot A has a greater median than Plot B, but Plot B has a greater mean. Plot B has a greater median than Plot A, but Plot A has a greater mean..

### Answers

The true statement is both the **mean and median** are** greater for Plot A **than for** Plot B..**

What is the true statement?

**Mean **is the average of a data set. **Median **is the number at the center of a dataset arranged in either ascending or descending order.

Mean for **plot A ** = (3 + 4 + 4 + 5 + 5 + 6 + 6 + 7 + 7 + 10) / 10 = 5.7

Median for **plot A ** = (5 + 6) / 2 = 5.5

Mean for **plot B** = (3 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 6 + 7) / 10 = 5.1

Median for **plot B ** = 5

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I don’t understand how to solve these :(

### Answers

**Answer:**

A.

3.2

B.

3.66

**Step-by-step explanation:**

Okay so I inserted a picture showing how to do everything I hope you pass! Have a great day!! Also ignore the answer for b on the paper that one is innocent the one on here is right

what is the slope of the line that passes through the points (-6,1) and (-6,-4)? write your answer in the simplest form.

### Answers

**Answer:**

Undefined

**Step-by-step explanation:**

-4-1/-6+6

Since the bottom adds up to zero and you cannot simplify a fraction with 0 as the denominator, the slope is undefined.

**Answer:**

Undefined

**Step-by-step explanation:**

Hi student! Let me help you out on this question.

**_________________ **

**-** - **- **- **- **- **- **- **- **- **- **- **- **- **- **- **- **- **- **-

We can find the slope, using the formula.

[tex]\mathrm{\cfrac{y2-y1}{x2-x1}}[/tex].

where:#1. x2 and x1 are **x-co-ordinates.**#2. y2 and y1 are **y-co-ordinates.**

Plugin the values.

[tex]\mathrm{\cfrac{-4-1}{-6-(-6)}}[/tex]

↪

*Do you see what I see?*

To find out, simplify further.

[tex]\mathrm{\cfrac{-3}{-6+6}}[/tex]. Simplifying completely results in.

[tex]\mathrm{\cfrac{-3}{0}}[/tex].

We know that we **cannot** divide by zero.

[tex]\therefore\mathrm{Slope=unde fined}}[/tex]. Which is our answer.

**Hope that this helped you out! have a good day ahead.**

**Best Wishes!**

[tex]\star\bigstar\textsf{Reach far. Aim high. Dream big.}\bigstar\star[/tex].

*◈◈-Greetings!-◆◆*

- **- **- **- **- **- **- **- **- **- **- **- **- **- **- **- **- **- **

**______________________**

If f(x) = 2x - 1 and g(x)=x²-3x-2, find (f+ g)(x).

### Answers

[tex]\text{Given that,}~ f(x) = 2x -1~ \text{and}~ g(x) = x^2- 3x -2 \\\\\text{Now,}\\\\~~~(f+g)(x)\\\\=f(x) + g(x)\\\\=2x-1 +x^2 -3x -2\\\\=x^2 -x -3[/tex]

**Answer:**

(f + g)(x) = x² - x - 3

**Step-by-step explanation:**

(f + g)(x)

= f(x) + g(x)

= 2x - 1 + x² - 3x - 2 ← collect like terms

= x² - x - 3 ← in standard form

Determine the relationship between the quantities on the given graph.

Total Wages

Wages Earned ($)

Time Worked (hours)

OA. The time worked depends on the wages earned.

OB. The wages earned depends on the time worked.

### Answers

OB

because its the most accurate

log8 2 + 3log8 2 + 1/2log8 16

step by step pls

### Answers

**Answer:**

2

**Step-by-step explanation:**

Given expression:

[tex]\log_82+3\log_82+\dfrac{1}{2}\log_816[/tex]

[tex]\textsf{Apply the Power law}: \quad n\log_ax=\log_ax^n[/tex]

[tex]\implies \log_82+\log_82^3+\log_816^{\frac{1}{2}[/tex]

Simplify:

[tex]\implies \log_82+\log_88+\log_84[/tex]

[tex]\textsf{Apply the Product law}: \quad \log_ax + \log_ay=\log_axy[/tex]

[tex]\implies \log_88+\log_8(2 \cdot 4)[/tex]

[tex]\implies \log_88+\log_88[/tex]

[tex]\implies 2\log_88[/tex]

[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]

[tex]\implies 2 \cdot 1[/tex]

[tex]\implies 2[/tex]

Answer :

[tex] \frac{21}{3} [/tex]

Explanation :

please look above for your answer .

please can you help me

### Answers

a= 47

b=60

c=37

d=130

e=38

**Answer:**

1. 47°

2. 60°

3. 37°

4. 130°

5. 38°

**Step-by-step explanation:**

2. an equilateral triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 180 / 3 = 60°

Scalar and Matrix Multiplication

### Answers

**Answer:**

multiply -4 by each element in the matrix

**Step-by-step explanation:**

-32

4

20

-36

33 POINTS!!!!! NEED ASAP

Part E

What does this show about the relationship between the two triangles?

Part F

Does this mean that triangle 1 is a right triangle? Why or why not?

### Answers

The relationship between the two **triangles** is that they are **congruent** as the sides are equal.

How to illustrate the triangle?

It should be noted that **congruence** simply means and the sides in a **triangle** are equal as well as the angles being identical.

Triangle 1 is not a right triangle rather, it's a **scalene triangle** since it's right angle isn't 90°.

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Which equation has the solutions x = startfraction 5 plus-or-minus 2 startroot 7 endroot over 3 endfraction?

### Answers

The **equation **that has the **solution **[tex]x = \frac{5 \pm \sqrt{7}}{3}[/tex] is 3x^2 - 10x + 6 = 0

How to determine the equation?

The **solution **is given as:

[tex]x = \frac{5 \pm \sqrt{7}}{3}[/tex]

The solution to a **quadratic equation **is

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

By comparing both **equations**, we have:

-b = 5

b^2 - 4ac = 7

2a = 3

Solve for b in -b = 5

b = -5

Solve for a in 2a = 3

a = 1.5

Substitute values for a and b in b^2 - 4ac = 7

(-5)^2 - 4 * 1.5c = 7

Evaluate

25 - 6c = 7

Subtract 25 from both sides

-6c = -18

Divide by - 6

c = 3

So, we have:

a = 1.5

b = -5

c = 3

A **quadratic equation** is represented as:

ax^2 + bx + c = 0

So, we have:

1.5x^2 - 5x +3 = 0

Multiply through by 2

3x^2 - 10x + 6 = 0

Hence, the **equation **that has the **solution **[tex]x = \frac{5 \pm \sqrt{7}}{3}[/tex] is 3x^2 - 10x + 6 = 0

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V

Next → Function Notation: Mastery Test

1

Select the correct answer from each drop-down menu.

A function is a relation where each input value is assigned to

The

one output value.

of a function is the set of all Input values, or x-values, for which the function is defined.

of a function is the set of all output values, or y-values, for which the function is defined.

for y.

The

To write the equation y= ax + b in function notation, substitute

Reset

Next

### Answers

It is to be noted that the blanks can only be filled with **f(x)**, **range**, and **domain**.

What are the complete sentences?

The **domain **of a function is the set of all input values, or x-values, for which the **function** is defined.

The **range **of a function is the set of all output values, or y-values, for which the function is defined.

To write the equation y = ax + b in function **notation**, substitute **f(x)** for y.

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[tex] [/tex] [tex] [/tex] [tex] [/tex][tex] [/tex] 2-10 ^_^

### Answers

**Answer:**

I guess this u should solve by urself

Genuinely confused rn

Greg has 4 shirts: a white one, a black one, a red one, and a blue one. He also has two pairs of pants, one blue and one tan. What is the probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants? Show your work.

im thinking its 1/4 x 1/2 = 1/8, please correct me if im wrong

### Answers

Using it's concept, it is found that the **probability **that he winds up wearing the white shirt and tan pants is of [tex]\frac{1}{8}[/tex].

What is a probability?

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem:

For the shirt, there is 4 outcomes, hence the probability of the **white shirt is 1/4**.For the pair of pants, there are 2 outcomes, blue or tan, hence the probability of **tan pants is 1/2**.

Since the shirt and the pants are **independent**, the **probability **is given by:

[tex]p = \frac{1}{4} \times \frac{1}{2} = \frac{1}{8}[/tex].

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**Answer:**

this is so you can mark the other person brainlists or whatever

**Step-by-step explanation:**

using this info rn

please help!! a regular pentagon ABCDE is shown. work out the size of angle x

### Answers

**Answer:**

36°

A+B+C+D+E=5C=(5-2)×180°=540°

C=540÷5=108°

since BC=CD

x = CDB = ½(180°-C)=½(180°-108°)=½72°=36°

Question 5 of 10

Which expressions are equivalent to the one below? Check all that apply.

64^x

A. 8^x •8^x

B. 8^2x

C. 8•8^2x

D.8^2•8^x

E. (8•8)^x

F. 8•8^x

### Answers

**Answer:** Option A, B, E are correct.

**A. **8^x •8^x = 64^x

**B.** 8^2x = 64^x

**C.** 8•8^2x = 8^{1 + 2x}

**D.**8^2•8^x = 8^{2 + x}

**E.** (8•8)^x = 64^x

**F.** 8•8^x = 8^{1 + x}

how many x-intercepts does the polynomial function y=(x-2)(x+3)^2 have?

### Answers

**Answer:**

2

**Step-by-step explanation:**

(x-2)(x+3)(x+3)

(x² + x - 6)(x+3)

x³ + 4x² - 3x - 18

we can see here it is cubic but 2 of the roots are the same

find the measure of the numbered angle in rhombus abcd

### Answers

**Answer:**

see below :)

M1=90°

M2=53°

M3=53°

M4=37°

Hope this helps:D

If A=(-1, 3] and B = [0, 4) then B-A

### Answers

I assume B - A means "the complement of A in B", or all the elements of B not belonging to A.

Then **B - A = (3, 4)**, since A ∩ B is the interval [0, 3] and we omit this from the parent interval B = [0, 4).

A car travels at 80km/h for 4 hours and then a speed of 100km/h for a further 2 hours .

1) Calculate the total distance travelled.

2) Calculate the average speed for the whole journey.

### Answers

**Answer:**

Total Distance = 520km

Average speed = 86.667km/h (to 3 decimal places).

**Step-by-step explanation:**

80 x 4 = 320km

100 x 2 = 200km

Total distance: 320km + 200km = 520km

Average speed: 520/6(hours) = 86.666

Find the hypotenuse of an isosceles right triangle when the legs each measure 3\sqrt{x} 2inches.

### Answers

The **hypotenuse **of the **right triangle **measures 3 units.

**How to find the hypotenuse?**

Here we know that both legs measure:

[tex]L =\frac{3}{\sqrt{2} }[/tex]

If we use the **Pythagorean theorem**, we will see that the **hypotenuse **H can be written as:

[tex]H^2 = (\frac{3}{\sqrt{2} } )^2 + (\frac{3}{\sqrt{2} } )^2 \\\\H^2 = \frac{9}{2} + \frac{9}{2} = \frac{18}{2} = 9\\\\H = \sqrt{9} = 3[/tex]

Then we conclude that the **hypotenuse **of the** right triangle** measures 9 units.

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John is driving a bicycle race 250 km long. After driving 34% of the race, find the

distance John has passed.

### Answers

**Answer: 85 km**

**Step-by-step explanation:**

250 x 0.34 = 85

Calculate √62 correct to 1 decimal place.

### Answers

**Answer:**

7.9

**Step-by-step explanation:**

7.87400787401

Which equation represents the slope-intercept form of the line below?

### Answers

that would be letter b

The answer is b.

y=mx+b, where b is the y intercept and m is the slope. for answer B, the y intercept is +8 and the slope is 1/2, which matches the graph shown.

Write the reciprocal of

a) 7/10

b)3.5

### Answers

**Answer:**

a)

[tex] \frac{10}{7} [/tex]

b)

[tex] \frac{10}{35} [/tex]

**Step-by-step explanation:**

The reciprocal of a number is the inverse of the number

**[tex] \frac{7}{10} = \frac{10}{7} (reciprocal)[/tex]**

**[tex]3.5 \: is \: also \: \frac{35}{10} [/tex]**

**[tex] \frac{35}{10} = \frac{10}{35} (reciprocal)[/tex]**

**[tex]you \: may \: choose \: to \: simplify \: to \: the \: lowest \: term \: depending \: on \: the \: question[/tex]**

Q7) I CAN FIND THE PROBABILITY OF AN EVENT WHEN THE OUTCOMES ARE EQUALLY LIKELY A bag contains 5 grapes, 2 bananas, and 6 avocados. One fruit is chosen at random. What is the probability an avocado is chosen? I a) 1/5 b) 6/7 c) 6/13 d) 2/13

### Answers

**Answer:**

c

**Step-by-step explanation:**

Avacado is 6 out of 5 + 2 + 6 fruits

6 out of 13 = 6/ 13

The pressure in a 28.0 L helium cylinder is 850 psi at 28.5 oC. The tank is emptied filling 3.75 L balloons at 14.0 oC and 102.6 kPa. How many balloons can be completely filled by emptying the helium cylinder?

### Answers

The **number **of **balloons **that can be completely filled by emptying the **helium cylinder** is **406.**

**Number of balloons to be filled by the cylinder**

The **number of balloons** to be filled by the **cylinder **is calculated by using general gas equation as shown below;

[tex]\frac{P_1V_1}{T_1} =n( \frac{P_2V_2}{T_2})[/tex]

where;

n is number of balloonsP1 = 850 psi P2 = 102.6 kPa = 14.88 psiT1 = 28.5⁰C = 301.5 KT2 = 14⁰C = 287 K

[tex]\frac{850 \times 28}{301.5} =n( \frac{14.88 \times 3.75}{287})\\\\78.94 = 0.194n\\\\n = 406[/tex]

Thus, the **number **of **balloons **that can be completely filled by emptying the **helium cylinder** is **406.**

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Can someone explain to me how the x in w(x) = 3x - 7 if w(x) = 14 is 7?

Let w(x) = 3x - 7 if w(x) = 14, find x.

### Answers

**Answer:**

see explanation

**Step-by-step explanation:**

given w(x) = 3x - 7 and w(x) = 14 then equating the two gives

3x - 7 = 14 ( add 7 to both sides )

3x = 21 ( divide both sides by 3 )

x = 7

Find the distance between (-4,-3) and (-2,0). round your answer to the nearest tenth.

### Answers

**Answer:**

3.61

**Step-by-step explanation:**

We need to use the distance formula for this:

Basically, we find the different between the the x points: -2-(-4)

Thats 2

Next we square 2 to get 4

Now we find the different between the y points: -3-0

Thats -3

Next we square -3 to get 9

Now, we add 9 to 4 to get 13

Finally, we take to square root of 13 to get 3.61

Have a nice day!

select the equation of a straight line that is parralell to the line 4y=3x+5

### Answers

A line that is **parallel **to another line will have the **same slope** as the original.

Let's start by putting the given line into slope-intercept form (y = mx + b, where m = slope and b = y-intercept).

4y = 3x + 5

y = 3/4x + 5/4

In this case, the slope of the original line is **3/4**. Therefore, a parallel line will also have a slope of **3/4**.

Hope this helps!