Mathematics High School

## Answers

**Answer 1**

**Answer:**

x = sqrt(32)

**Step-by-step explanation:**

Since this is a right triangle, we can use the Pythagorean theorem

a^2+ b^2 = c^2

7^2 + x^2 = 9^2

49+x^2 = 81

Subtract 49 from each side

x^2 = 81-49

x^2 =32

Take the square root of each side

sqrt(x^2) = sqrt(32)

x = sqrt(32)

**Answer 2**

**Answer:**

C

**Step-by-step explanation:**

You can use the Pythagorean Theorem (a*² + b² = c²*) to solve this problem.

*a* and *b* are the legs, while *c* is the hypotenuse, or the longest side. In this case, *x *and 7 are the legs, while 9 is the length of the hypotenuse.

*x² + 7² = 9²*

*x² + 49 = 81*

*x² = 32*

*x = √32*

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## Related Questions

Which expression is equivalent to -8?

### Answers

**Answer:**

2^-3

**Step-by-step explanation:**

**Answer:**

The answer is the second one: [tex](-1/2)^{-3}[/tex]

**Step-by-step explanation:**

1) When an exponent is negative, we must 'flip' the term before applying the exponent.

[tex](-1/2)^{-3}[/tex] = [tex](-2/1)^3[/tex]= [tex]-2^3[/tex]

2) Next, we need to cube two. Remember, the negative number does not apply yet!

[tex]-2^3[/tex] = -8

3) Thus, we get our answer. -8.

I hope this help, firend!!

PLZ ASAP ITS FOR A TIMED TEST THAT DETERMINES EVERYTHING I BEGGGG..\There are seven roads that lead to the top of a hill. a How many different ways are there to reach the top and then go back down? Answer:

### Answers

**Answer:**

**42**

**Step-by-step explanation:**

For this it's very simple

This is a permutations question so -->

7 roads that go to the top and you want to find how many ways you can go back

7x7 since the ways you go down it is unrestricted BUT THIS IS NOt YOUR FINAL ANSWER

Since you cannot repeat the roads after one whole run, your equation is actually 7x6 giving you 42

Hope this helps

**Answer:**

**The correct answer is 49**

3x√64= please help meee

### Answers

**Answer:**

I think the answer is 2.7

**Step-by-step explanation:**

3x√64

√64=8

3x=8

x=8/3

x=2.7

If you simply it to becomes 3x8 = so the answer is 24

If 180°<α<270°, cos α= −8/17, 270°<β<360°, and sin β= −4/5, what is sin(α+β)?

### Answers

**Answer:**

[tex]\sin(\alpha+\beta) = -0.153[/tex]

**Step-by-step explanation:**

Let determine the angles behind each trigonometric expression:

[tex]\cos \alpha = -\frac{8}{17}[/tex]

[tex]\alpha = \cos^{-1}\left(-\frac{8}{17} \right)[/tex]

Given that [tex]180^{\circ}< \alpha < 270^{\circ}[/tex], the value of [tex]\alpha[/tex] is:

[tex]\alpha \approx 241.928^{\circ}[/tex]

[tex]\sin \beta = -\frac{4}{5}[/tex]

[tex]\beta = \sin^{-1}\left(-\frac{4}{5} \right)[/tex]

Given that [tex]270^{\circ}< \beta <360^{\circ}[/tex], the value of [tex]\beta[/tex] is:

[tex]\beta \approx 306.870^{\circ}[/tex]

The sine function of the sum of angles can be determined by the following identity:

[tex]\sin(\alpha + \beta)=\sin \alpha \cdot \cos \beta + \sin \beta \cdot \cos \alpha[/tex]

If [tex]\alpha \approx 241.928^{\circ}[/tex] and [tex]\beta \approx 306.870^{\circ}[/tex], then:

[tex]\sin (241.928^{\circ}+306.870^{\circ}) = (\sin 241.928^{\circ}) \cdot (\cos 306.870^{\circ}) + (\sin 306.870^{\circ})\cdot (\cos 241.928^{\circ})[/tex][tex]\sin(241.928^{\circ}+306.870^{\circ}) = -0.153[/tex]

A solid shape is made from centimetre cubes.

Here are the plan, side elevation and

Centimetre cubes are added to

front elevation of the shape.

make this cuboid.

Plan Side elevation Front elevation

40

4 cm

3 cm

How many cubes are added?

Write your final answer as,... cubes are added.

### Answers

**Answer:**

30 cubes are added

**Step-by-step explanation:**

The image of the solid shape is attached.

From the Plan, Side elevation and Front elevation, the number of cubes needed to make the shape is 18 blocks. From the front elevation, 12 blocks is needed (4 * 3 blocks) while from the side elevation 6 blocks are needed given a total of 18 blocks.

The number of blocks needed to make the cuboid = 4 * 4 * 3 = 48 cm cubes.

Therefore the number of cubes to be added = 48 cubes - 18 cubes = 30 cubes.

30 cubes are added

The **number of cubes** that are added is 30.

**What is Cube?**

A **cube's** form is occasionally referred to as **"cubic.**" Another way to put it is that a block with uniform length, width, and height is regarded to be a **cube**. It also contains 12 edges and 8 vertices, with 3 of the edges coming together at a single vertex point. Examine the illustration below, identifying the faces, edges, and vertices. It is also referred to as a right rhombohedron, an **equilateral cuboid,** and a square parallelepiped. One of the platonic solids, the cube is a convex polyhedron with all of its faces being square. The** cube** has either cubical symmetry or octahedral symmetry. The square prism is a specific instance of a cube.

From the Plan, Side elevation, and Front elevation, the number of **cubes **needed to make the shape is 18 blocks. From the front elevation, 12 blocks are needed **(4 * 3 blocks)** while from the side elevation 6 blocks are needed given a total of 18 blocks.

The **number of blocks** needed to make the **cuboid**

= 4 * 4 * 3 = 48 cm **cubes.**

Therefore the number of** cubes** to be added

= 48 cubes - 18 cubes

= 30 cubes.

30 cubes are added.

Hence, The **number of cubes** that are added is 30.

To learn more about, cubes, visit;

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Students in an introductory statistics course were asked the following questions as part of a class survey:(1) What is your gender, male or female?(2) On average, how many hours of sleep do you get per night?(3) What is your bedtime: 8pm-10pm, 10pm-12am, 12am-2am, later than 2am?(4) How many countries have you visited?(5) On a scale of 1 (very little) - 5 (a lot), how much do you dread this semester? Identify the variables in the survey. Classify each variable as numerical or categorical. For each numerical variable, identify whether it is continuous or discrete. For each categorical variable, identify whether it is nominal or ordinal.

### Answers

**Answers:**

Gender = **categorical, nominal variable**

Sleep length = **numerical, continuous**

Bedtime = **categorical, ordinal**

Number of countries visited = **numerical, discrete**

Scale of dreading semester = **categorical, ordinal**

=========================

Explanation:

Gender is categorical because there are two categories or labels, male or female. It is nominal because we simply attach names to each label and we can't sort them or order them from highest to lowest. There is no ranking for gender.

Sleep length is numerical as it deals with numbers. I put continuous because someone could write 2.5 hours or 3.75 hours. If whole numbers are only allowed, then the variable would be discrete.

The bedtime portion is categorical as each time slot is a category. Like with the first part, they are simply labels. We can order them however from earliest to later on, which is why this variable is ordinal.

The number of countries visited is numeric as expected, and it's also discrete because we can't visit 0.1 of a country. By "visit", I mean step foot in any part of the country for any length of time. It does not mean you have to explore every square inch of the territory.

The last part is categorical and ordinal. The scale ranking is ordered for us from 1 to 5. Despite the fact we have numbers here, the data is not numerical as the numbers 1 through 5 represent labels of "very little" through "a lot".

Work out the size of angle x

### Answers

Answer:

x = 117 degrees

Step-by-step explanation:

A triangle has 180 degrees in total.

A straight line is also 180 degrees in total.

180 - 101 = 79

Angles inside the triangle

79 + 38 = 117

180 - 117 = 63

63 degrees is the missing angle

x = 180 - 63

x = 117

**Answer:**

x = 117°

**Step-by-step explanation:**

First, find the angle the supplements angle 101°.

Using the supplementary angle (angles that add up to 180°).

180° - 101° = 79°

We now have two interior angles inside the triangle, 38° and 79°.

A triangle's total angle measures 180° in total.

So,

? + 38° + 79° = 180°

? + 117° = 180

? = 180° - 117°

? = 63°

Now like the first step we did, use the supplementary angle theorem to find x.

x + 63° = 180°

x = 180° - 63°

x = 117°

The volume of an object is equal to the ratio of its mass to density, V = StartFraction m Over d EndFraction. The mass of a spherical grape is 8.4 grams and its density is 2 grams per cubic centimeter.

What is the radius of the grape? Round to the nearest tenth of a centimeter.

1.0 cm

1.5 cm

1.9 cm

2.1 cm

### Answers

**Answer:**

R=1.0 cm

**Step-by-step explanation:**

V=m/d

V=8.4g/(2g/cm³)=4.2cm³

**V=4 π R³/3** ; π≅3.14

R³ =3V/(4 π)=3*4.2cm³/(4*3.14)=12.6cm³/12.56 ≅ 1.0 cm³

=>**R=∛(1.0 cm³) =1.0 cm**

The **radius** of the spherical grape is 1.0 cm.

What is density?

**Density **refers to the measurement of the amount of mass of a substance per unit of **volume**.

This measurement of a pure substance has the same value as its mass **concentration**. Densities vary with different materials or substances.

i.e., V=m/d

Given that, the mass of a **spherical grape** is 8.4 grams and its **density** is 2 grams per cubic centimeter.

V = 8.4g/(2g/cm³) = 4.2cm³

V = 4 π R³/3

R³ =3V/(4 π) = 3*4.2cm³/(4*3.14)=12.6cm³/12.56 ≅ 1.0 cm³

R =1.0 cm

Hence the **radius** of the spherical grape is 1.0 cm.

Learn more about **density**, click;

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what number decreased by 6 equals 3 times the number

### Answers

**Answer:**

-3

**Step-by-step explanation:**

x-6=3x

2x=-6

x=-3

The required number is **-3** **decreased **by **6** equals **3 times**.

A **number **to be determine when **decreased **by **6** equals **3 times** the number.

What is arithmetic?

it explores the numbers of operations according to the statements.

Let the number be x,

Now,

x-6=3x

x= -3

Thus, the required number is **-3** **decreased **by **6** equals **3** **times**.

Learn more about **arithmetic **here:

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Fiona draw a circle with a diameter of 14 meters. What is the area of Fiona circle?

### Answers

**Answer:**

153.938 meters

**Step-by-step explanation:**

The area of a circle is Pi * (Radius)^2. The radius is the diameter/2.

14/2=7

Pi * (7)^2

153.938 m

**Answer:**

154 cm^2

**Step-by-step explanation:**

[tex]d =14\\Area = \pi \times r^2\\r = d/2\\r = 14/2\\r= 7\\A = 22/7 \times 7^2\\\frac{22}{7} \times 49\\Simplify\\\frac{22}{1} \times 7\\Area =154[/tex]

[tex]A =\frac{1}{4} \pi \times d^2\\A = \frac{1}{4} \times \frac{22}{7} \times14^2\\A = 1/4\times22/7\times196\\A = 154cm^2[/tex]

∠7 and ∠8 are linear angles and m∠7 is 4 times that of m∠8. Find m∠8 please show work! i already know the answer but I need the work so that i can understand it :) (the answer is 36 degrees)

### Answers

**Answer:**

36°

**Step-by-step explanation:**

Let m∠8 = x°

Therefore, m∠7 = 4x°

Since, ∠7 and ∠8 are linear angles.

Therefore,

m∠7 + m∠8= 180°

4x° + x° = 180°

5x° = 180°

x° = 180°/5

x° = 36°

x = 36

Hence,

m∠8 = 36°

How do you do this? please help me

### Answers

**Answer:**

f = 10, g = 4.8 cm

**Step-by-step explanation:**

Area of ABCE = 60 cm²

Area of ABCD = 48 cm²

So,

Area of ADE = 60-48

=> 12 cm²

Area of ADE = [tex]\frac{1}{2} (Base)(Height)[/tex]

**Where Area = 12 cm², Base = 4 cm**

12 = [tex]\frac{1}{2}(4)(Height)[/tex]

Height = 12-2

Height = 10 cm

Where Height is AD

So, **AD = 10 cm**

Also, * AD is parallel and equal to BC*[tex](f)[/tex]

So,

**f = 10 cm**

**Now, Finding g**

Area of ABCD = [tex]Base * Height[/tex]

**Where Area = 48 cm², Base = 10 cm**

48 = 10 * Height

Height = 48/10

Height = 4.8 cm

Whereas, Height is g

So, **g = 4.8 cm**

What are the values of the variables in the triangle below? If your answer is not an integer, leave it in simplest radical form. The diagram is not drawn to scale.

### Answers

**Answer:**

x = 12y = 4√3

**Step-by-step explanation:**

**To find x we use cosine**

cos∅ = adjacent / hypotenuse

x is the adjacent

8√3 is the hypotenuse

cos 30 = x / 8√3

x = 8√3 cos 30

x = 12

**To find y we use sine**

sin∅ = opposite / hypotenuse

y is the opposite

8√3 is the hypotenuse

sin 30 = y / 8√3

y = 8√3 sin 30

y = 4√3

Hope this helps you

In 9 minutes, Ivanna can type 36 words. What is her rate in words per minute?

### Answers

**Answer:**

4

**Step-by-step explanation:**

9 divided by 36

**Answer:**

4 words/minute

**Step-by-step explanation:**

Since we need words per minute, we divide the number of words by the number of minutes.

words/minute = (36 words)/(9 minutes) = 4 words/minute

Plz help asap this table represent a quadratic function with a vertex a (1,2) what is the average rate of change for the interval from x=5 to x=6

### Answers

Answer:

9

Step-by-step explanation:

Given that (1, 2) is the vertex of the function represented by the table of values above, the rate of change for the interval from x = 5 to x = 6.

f(5) = 18

f(6) = ?

=>Find f(6) using the vertex form function, f(x) = a(x - h)² + k

Where, h and k are the given vertex of the function = (1, 2).

h = 1, k = 2

Thus,

f(x) = a(x - 1)² + 2

Find the value of a by using any of the points given in the table.

Using (3, 6), we have the following,

6 = a(3 - 1)² + 2

6 = a(2)² + 2

6 = 4a + 2

Subtract 2 from both sides

6 - 2 = 4a

4 = 4a

Divide both sides by 4

1 = a

a = 1

Let's find f(6) using f(x) = a(x - 1)² + 2

Plug the value of a and x

f(6) = 1(6 - 1)² + 2

f(6) = 25 + 2

f(6) = 27

==>Find the rate of change/slope

f(5) = 18

f(6) = 27

Rate of change =

[tex] \frac{f(6) - f(5)}{6-5} [/tex]

[tex] \frac{27- 18}{6-5} [/tex]

[tex] \frac{9}{1} [/tex]

Rate of change = 9

NEED HELP ASAP!!!! I will reward you as the most brainliest!

### Answers

**Step-by-step explanation:**

v = 1/3πr²h

1/3×314/100×4×4×7

11,722.666round off

11722.67

formula =v= 3.14×radius×radius ×height ×3

**Step-by-step explanation:**

pie×radius×squared ×7×3

=117.29

when we round it to the nearest hundredth

its=117.29m squared

Write the unit rate for the situation.

read 80 pages in 2 hours

20 pages/h

40 pages/h

8 pages/h

160 pages/h

### Answers

**Answer:**

40 pages / hour

**Step-by-step explanation:**

Take the number of pages and divide by the number of hours

80 pages/ 2 hours

40 pages / hour

Which set of ordered pairs represents a function?

{(9,8),(-1,7),(-1, -9), (3, -1)}

{(9,5),(4,6), (9,8),(-6,9)}

{(-8,0),(-8,2), (5, -7),(-2,-9)}

{(2,9),(-4,-6), (9,6), (0,6)}

### Answers

**Answer:**

{(2,9),(-4,-6), (9,6), (0,6)}

**Step-by-step explanation:**

A function has no repeating inputs (x-values) in a given set of ordered pairs.

**The bottom set is a function. There are no repeating inputs in the given pairs. **

**All other sets have a ****repeating input****; Therefore ****they are not functions****.**

{(9,8),(**-1**,7),(**-1**, -9), (3, -1)}

{(**9**,5),(4,6), (**9**,8),(-6,9)}

{(**-8**,0),(**-8**,2), (5, -7),(-2,-9)}

*Brainilest Appreciated. *

Can you work out which is the odd one out?

### Answers

**Answer:**

c is the odd one.

**Answer:**

C

**Step-by-step explanation:**

A loaf of bread that is baked today costs $7. All of the bread baked yesterday is 40% off.

Tobin has $5. He wants to know if $5 is enough to purchase a loaf of yesterday's bread.

How can Tobin find the price of a loaf of

yesterday's bread? Complete the statement

The price of ?

equals

the price of ?

minus

the discount

### Answers

The price of** yesterday's bread** equals the price of** today's bread **minus the **discount.**

The **price **of **yesterday's bread **is equal to the price of **today's bread **less the dollar equivalent of the **discount.**

dollar equivalent of the **discount = **40% X $7

= 0.4 X $7 = $2.80

P**rice **of **yesterday's bread = **$7 - $2.80 = $4.20

To learn more about how to calculate **discounts,** please check: https://brainly.com/question/9350849

At a fruit market, John bought some oranges for a total of $20. Jenny visited another stall,

and bought 10 more oranges for the same price. Given that the difference in price per orange

was 10 cents, how many oranges did John purchase?

### Answers

**Answer:**

40 oranges.

**Step-by-step explanation:**

We have the following information:

John bought "x" oranges for $ 20 plus each orange for John costs 20 / x.

After Jenny bought x + 10 oranges for mimes $ 20 and also each orange for Jenny costs 20 / (x + 10). They tell us that the difference in price was 10 cents, that is to say 0.10 dollars, we would have the following:

20 / x - 20 / (x + 10) = 0.10

solving:

20x + 200 - 20 * x = 0.10 (x² + 10 * x)

x² + 10 * x-2000 = 0

we factor

(x + 50) (x-40) = 0

x + 50 = 0 => x = -50, this answer cannot be

x - 40 = 0 => x = 40, it is a viable answer so John bought a total of 40 oranges.

Williams says that 15 years from now, his age will be 3 times his age 5 years ago, if x represent Williams present age, complete the following sentence.

### Answers

**Answer:**

This is duplicate question

**Step-by-step explanation:**

https://brainly.com/question/8713027

link is here for answer

**The equation is x+15=3(x-5)**

**He is 15.**

What is the value of x

### Answers

**Answer:**

[tex]x=20[/tex]

**Step-by-step explanation:**

Since angle RTS is a right angle, we have three similar triangles.

Thus, [tex]\frac{x}{25} = \frac{16}{x}[/tex]

Cross Products, [tex]x^2=400[/tex]

Take the square root: [tex]x=20[/tex]

**Answer:**

x=20

**Step-by-step explanation:**

RTS is a right triangle so you cross multiply

SOLVE

Which of the following ordered pairs are equal? Write with reason

(a) (2, 3) and (4,2)

### Answers

**Answer: **(2, 3) and (4,2) are not equal.

**Step-by-step explanation:**

An ordered pair is something like (x, y)

and two pairs (x1, y1) and (x2, y2) are only equal if x1 = x2 and y1 = y2

in this case, we have (2, 3) and (4, 2)

you can see that in the pairs the value of x is different, and the value of y is also different. Then we have that the pairs can not be equal.

Which function represents g(x), a reflection of f(x) = Two-fifths (10)x across the x-axis? g(x) = Negative two-fifths(10)x g(x) = Negative two-fifths (one-tenth) Superscript x g(x) = Two-fifths (one-tenth) Superscript negative x g(x) = Two-fifths(10)-x

### Answers

**Answer:**

The correct option is;

g(x) = Negative two-fifths(10)x

**Step-by-step explanation:**

The rule for the reflection across the x-axis is as follows;

Reflection about the x-axis

Pre-image point before reflection = (x, y)

Point of image after reflection = ((x, -y)

Therefore, the x coordinate remains the same while the y coordinate changes sign

For which given that f(x) = y = 2/5(10)x and g(x) = Reflection of f(x) across the x-axis, we have

Reflection about the x-axis

Pre-image point before reflection = (x, f(x))

Point of image after reflection = (x, g(x))

Hence g(x) = -f(x) = -2/5(10)x.

**Answer:**

A

**Step-by-step explanation:**

evaluate this please

### Answers

**Answer:**

**Step-by-step explanation:**

| |-11| - |4 - 15| |

= |11 - |-11| |

= |11 - 11|

= |0| = 0

**Answer:**

**Step-by-step explanation:**

First find the absolute value inside the large absolute value

| -11| = 11

|4-15| = |-11| = 11

| 11 - 11| = |0| = 0

1. Which of the following measurements could be the three side lengths of a right triangle? a. 4 cm, 5 cm, 9 cm b. 12 cm, 20 cm, 25 cm c. 18 cm, 24 cm, 30 cm d. 2 cm, 3 cm, 5 cm

### Answers

**Answer:**

b and c

**Step-by-step explanation:**

The Triangle Inequality Theorem lets us know that the sum of the two shortest sides of the triangle must be **greater than** the third side of the triangle.

In both A and D, the sum of the shortest two sides are **equal to**, not **greater than** the third side, so they will not form a triangle.

In B, 12+20 is 32, which is greater than 25. And in C, 18+24 is 42, which is greater than 30, so they both will form a triangle.

Using the **Pythagorean **Theorem, it is found that possible **side lengths** of a right triangle are given by:

**c.** 18 cm, 24 cm, 30 cm

What is the Pythagorean Theorem?

The Pythagorean Theorem relates the length of the **legs **[tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

The length of the hypotenuse is always greater than the length of the legs. The Pythagorean Theorem has to hold true, which holds only for **option C**, as:

18² + 24² = 30²

900 = 900

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Find the area and perimeterof a square with a side length of [tex]2\sqrt{3} + 6\sqrt{7}[/tex] inches

### Answers

**Answer:**

**Step-by-step explanation:**

Perimeter

P = 4s

P = 4*(2*sqrt(3) + 6*sqrt(7) )

P = 8*sqrt(3) + 24*sqrt(7)

Area

A = s^2

A = (2sqrt(3) + 6sqrt(7) )(2 sqrt(3) + 6sqrt(7) )

F:= (4*sqrt(3)^2 = 16 * 3 = 48

O:= 2sqrt(3) * 6sqrt(7) ) = 12sqrt(21)

I := 6*sqrt(7)*2 sqrt(3) = 12 sqrt(21)

L:=6*sqrt(7) ^2 = 36 * 7 = 252

The answer is 300 + 24*sqrt(21)

**Answer:**

**Step-by-step explanation:**

area=side ²=(2√3+6√7)²=4×3+36×7+2×2√3×6√7=12+252+24√21=264+24√21

Mrs. Brown has 11 more boys than girls in her class and has a total of 28 students. Which of the following systems of equations could be used to solve this problem?

### Answers

**Answer:**

g=number of girls in the class b=number of boy in the class

g+b=28

g=11+b

Fifteen women can weed a piece of land in

12 days. How many more women will be

required to clear the same land in10 days

### Answers

**Answer:**

**Brainliest**** ****please**

**Step-by-step explanation:**

15 women= 12days

find 10 days,

12÷10×15= 18women in ten days

**how**** ****many**** ****more**** ****women****,**** ***subtract*** **18 women and 15 women

=3 is the answer