A sphere has a height of 26. Find the surface area, volume and density (D=m/v , where m is 72)

Answers

Answer 1

Answer:

Surface Area: 2123.72

Volume: 9202.77

Density: 0.0078

Step-by-step explanation:

For a sphere, the height is the diameter.

Also we know the radius is half of the diameter.

Since height is 26, diameter is 26 as well. Thus, radius is half of 26, which is 13.

Formulas:

Surface area of sphere = 4πr^2

Volume of sphere = [tex]\frac{4}{3}\pi r^3[/tex]

Density = mass/volume

Firstly, the surface area:

[tex]4\pi r^2\\=4\pi (13)^2\\=2123.72[/tex]

Next, the volume:

[tex]\frac{4}{3}\pi r^3\\=\frac{4}{3}\pi (13)^3\\\\=9202.77[/tex]

Lastly, density:

[tex]\frac{Mass}{Volume}\\=\frac{72}{9202.77}\\=0.0078[/tex]

*Note: all answers are given as is since no units were given


Related Questions

Which decimal is equivalent to -3 1/8

Answers

Answer:

-3.125

Step-by-step explanation:

Answer: this is the correct answer -3.125

(x^2-2)^2-10(x^2-2)+21=0 find one value of x that is a solution to the equation

Answers

Answer:

x=3; x=-3; x=√5; x=-√5

Step-by-step explanation:

Final answer:

The equation can be simplified by treating (x^2 - 2) as y. Solving the quadratic equation for y results in y = 4 and y = 7. By substituting these back into the equation and solving for x, we find x = ±sqrt(6) and x = ±sqrt(9). Therefore, one possible solution for x is sqrt(6).

Explanation:

The equation provided is a quadratic in the form of x. In this case, let's take: (x^2 - 2) = y. Therefore the equation can be rewritten as: y^2 - 10y + 21 = 0. In order to find the roots of the equation, we should use the quadratic formula: y = [10 ± sqrt((10)^2 - 4*1*21)] / (2*1), which gives us y = 4 and y = 7. Now we substitute back y = (x^2 - 2). This will form two more quadratic equations: x^2 - 2 = 4 and x^2 - 2 = 7. Solving these, we get x = ±sqrt(6) and x = ±sqrt(9). So, one value of x that is a solution to the equation could be sqrt(6).

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A school bus can hold no more than 40 people. If there are 6 teachers on the bus, write and solve an inequality that shows how many students can be on the bus. Graph the solution on the number line.

Answers

Answer:  34 kids in all

Step-by-step explanation:

: 40 - 6 = 34

0            6                              34

|------------|----------------------------|

The bus can hold no more than 40 people. 6 are already on so at most, there can be 34 others on board. But the number doesn’t have to be exact.

Faith Franklin sells furniture and earns 8% commission on her total sales. Last month she had $33,500 in sales. How much did she earn?

$2,976.00

$2680.00

$3,015.00

$3685.00

Answers

Answer:

$2680.00

Step-by-step explanation:

We are informed that Faith Franklin sells furniture and earns 8% commission on her total sales. She sold $33,500 last month. We are required to determine her earnings for that month;

We simply evaluate 8% of  $33,500

[tex]\frac{8}{100}*33500=2680[/tex]

Therefore, she earned $2680.00

Please help me with this. TWO LINES MEET AT A POINT THAT IS ALSO THE ENDPOINT OF TWO RAY'S. SET UP AND SOLVE THE APPROPRIATE EQUATIONS FOR m AND N. ​

Answers

Answer:

m=47, n=52

Step-by-step explanation:

m is equal to 90-43 since 43+m is a right angle (straight angle 180 is composed of two right angles). n is equal to 90-38. If you solve of the missing angle not given a variable, you find n as well because opposite angles are congruent and have the same measure.

A real estate agent received a 6% commission on the selling price of a house. If his commission was $8,880, what was the selling price of the house?

Answers

Answer:

6% x = 8,880 : x = selling price of house.  

x = $148,000 : solve for x

Step-by-step explanation:

Final answer:

The selling price of the house can be calculated by dividing the commission ($8,880) by the commission rate (0.06). This gives a selling price of $148,000.

Explanation:

To solve this problem, you need to understand that the 6% commission the real estate agent received is based on the selling price of the house. You can find the selling price by dividing the commission by the percentage commission expressed as a decimal.

Here's the step-by-step solution:

Convert the 6% commission rate to a decimal by dividing 6 by 100, which gives 0.06.Next, divide the commission amount ($8,880) by the commission rate (0.06). Using this calculation, $8,880 / 0.06, we find that the selling price of the house is $148,000.

So, the selling price of the house on which the agent earned an $8,880 commission at a rate of 6% was $148,000.

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On a quiz show you've made it to the final round. The host explains to you that you can choose from 2 prize plans. In Plan A, you'll win $1,280 guaranteed, plus $40 more for each final round question you answer correctly. Under Plan B, you'll win only $800 guaranteed, but $100 for each question.Complete the following statements (use proper number formatting, such as commas):
The plans will pay the same at
correct questions.

The amount they'll pay at that number of questions is $
.

You think you can answer 9 questions correctly. Which plan should you choose?

Answers

D is the answer but I’m not sure

Solve the equation below for x.
-1/2(3x-4)=11

Answers

Answer:

x=-6

Step-by-step explanation:

You are given the equation

[tex]-\dfrac{1}{2}(3x-4)=11[/tex]

First, multiply it by 2 to get rid of fraction:

[tex]-(3x-4)=22[/tex]

Now open the brackets:

[tex]-3x+4=22[/tex]

Subtract 4 from both sides:

[tex]-3x+4-4=22-4\\ \\-3x=18[/tex]

Multiply it by -1:

[tex]3x=-18[/tex]

and divide by 3:

[tex]x=-6[/tex]

Answer:

[tex]\large\boxed{x=-6}[/tex]

Step-by-step explanation:

[tex]-\dfrac{1}{2}(3x-4)=11\qquad\text{multiply both sides by (-2)}\\\\(-2\!\!\!\!\1\diagup^1)\cdot\left(-\dfrac{1}{2\!\!\!\!\1\diagup_1}\right)(3x-4)=(-2)\cdot11\\\\3x-4=-22\qquad\text{add 4 to both sides}\\\\3x-4+4=-22+4\\\\3x=-18\qquad\text{divide both sides by 3}\\\\\dfrac{3x}{3}=-\dfrac{18}{3}\\\\x=-6[/tex]

It costs $120 to have a party for 9 people at the skating rink. The cost includes a charge of ,$10 for each person attending the party plus the price of a cake.
How much does the cake cost?

Answers

Answer:

The cake costs $30

Step-by-step explanation:

9(10)=90

120-90=30


Which of the following is a sum of cubes?
A)3x^3+8y^6
B)8x^3-27y^6
C)125x^6-9y^3
D)x^3+8y^6

Answers

Answer:

D) [tex]x^3+8y^6[/tex]

Step-by-step explanation:

We have been given four choices.

A) [tex]3x^3+8y^6[/tex]

B) [tex]8x^3-27y^6[/tex]

C) [tex]125x^6-9y^3[/tex]

D) [tex]x^3+8y^6[/tex]

Now we need to find about which of the above choices is a sum of cubes.

Basically we need to check which one of the given choices can be represented in cubic form along with addition sign.

3 and 9 can't be written in cubic form unless we use radical numbers.

So the only choice left is D)

D) [tex]x^3+8y^6[/tex]

[tex]=x^3+2^3(y^2)^3[/tex]

[tex]=x^3+(2y^2)^3[/tex]

which is clearly visible as sum of cubes.

Hello!

The answer is:

D) [tex]x^{3}+8y^{6}[/tex]

Why?

We are looking for the expression that can be obtained from a sum of cube factoring, the form of the sum of cubes will be:

[tex]a^{3}+b^{3}=(a+b)(a^{2} -ab+b^{2})[/tex]

The only option that matches with the sum of cubes form is the last option,

D) [tex]x^{3}+8y^{6}[/tex]

and it can be rewritten as the following expression:

[tex]x^{3}+8y^{6}=x^{3}+(2y^{2})^{3}\\\\x^{3}+(2y^{2})^{3}=(x+2y^{2})(x^{2}-2xy^{2}+(2y^{2})^{2})\\\\(x+2y^{2})(x^{2}-2xy^{2}+(2y^{2})^{2})=(x+2y^{2})(x^{2}-2xy^{2}+4y^{4})\\\\(x+2y^{2})(x^{2}-xy^{2}+4y^{4})=x*x^{2}-2x^{2}y^{2}+2xy^{4}+2x^{2}y^{2}-2xy^{4}+8y^{6}\\\\x*x^{2}-2x^{2}y^{2}+2xy^{4}+2x^{2}y^{2}-2xy^{4}+8y^{6}=x^{3}+8y^{6}[/tex]

Therefore, we have that:

[tex]x^{3}+8y^{6}=x^{3}+(2y^{2})^{3}=(x+2y^{2})(x^{2}-2xy^{2}+(2y^{2})^{2})=x^{3}+8y^{6}[/tex]

Hence, the correct answer is:

D) [tex]x^{3}+8y^{6}[/tex]

Have a nice day!

25 POINTS PLEASE HELP
YOU CAN CHOOSE MORE THAN ONE

Select all the correct answers.
A survey of 30 students each from three different high schools was conducted to find the number of hours they spent every month on volunteer work. Based on the median values of the data sets, represented here as dot plots, which conclusions are true?




The students in school 2 generally spend more time doing volunteer work than the students in school 1.
The students in school 1 generally spend more time doing volunteer work than the students in school 2.
The students in school 1 generally spend more time doing volunteer work than the students in school 3.
The students in school 1 generally spend less time doing volunteer work than the students in school 3.
The students in school 3 generally spend more time doing volunteer work than the students in school 2.

Answers

From the information given, it is true to state that:

"The students in school 1 generally spend more time doing volunteer work than the students in school 2." (Option B)

What is a dot plot?

In statistics, a dot plot, also known as a dot chart is a type of histogram or histogram-like chart that is used to represent data that is relatively small.

It is best used for indicating the statistical relationship between the data and its clusters, outliers, and gaps.

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School 2 students generally spend more time on volunteer work than School 1, while School 1 students tend to spend more time than School 3.

Based on the dot plots representing the number of hours spent on volunteer work by students from three different high schools, we can draw some conclusions about the median values of the data sets.

Firstly, comparing School 1 and School 2, it appears that students in School 2 generally spend more time doing volunteer work. This conclusion is supported by the higher frequency of dots in the higher hour range in School 2 compared to School 1.

Next, comparing School 1 and School 3, it seems that students in School 1 generally spend more time on volunteer work. The dot plot for School 1 shows a higher frequency of dots in the higher hour range compared to School 3.

In summary, students in School 2 generally spend more time doing volunteer work than those in School 1, while students in School 1 tend to spend more time on volunteer work than those in School 3.

The sum of the degree measures of any triangle is 180. In a particular isosceles triangle the degree measure of the vertex angle is 112. Find the measure of each base angle

Answers

Answer:

34

Step-by-step explanation:

Each of the base angles = x

x + x + 112 = 180                Subtract 112 from both sides. Simplify the left side.

2x + 112 - 112 = 180 - 112    Simplify

2x = 68                              Divide by 2

2x/2 = 68/2                       Simplify

x = 34

Each of the base angles = 34 degrees.

Graph 8x-2y=-16........

Answers

[tex]8x - 2y = - 16 \\ \\ 1. \: 2(4x - y) = - 16 \\ 2. \: 4x - y = - \frac{16}{2} \\ 3. \: 4x - y = - 8 \\ 4. \: 4x = - 8 + y \\ 5. \: 4x = y - 8 \\ 6. \: x = \frac{y - 8}{4} [/tex]

Find the area of the shaded region. Leave your answer in terms of pi.

A. (243pi+162) ft^2
B. (243pi-162) ft^2
C. (27pi+162) ft^2
D. (27pi-162) ft^2

Answers

ANSWER

A. (243pi+162) ft^2

EXPLANATION

The area of the shaded region is the sum of the area of the major sector and the area of the isosceles triangle.

Area of major sector

[tex] = \frac{360 - 90}{360} \times \pi \times {18}^{2} [/tex]

[tex] = 243\pi {ft}^{2} [/tex]

The area of the isosceles triangle is calculated using the formula;

[tex] = \frac{1}{2} {r}^{2} \sin( \theta) [/tex]

[tex]= \frac{1}{2} \times {18}^{2} \sin(90 \degree)[/tex]

[tex] = 162 {ft}^{2} [/tex]

The area of the shaded region

[tex] = (243\pi + 162) {ft}^{2} [/tex]

The correct answer is A.

Answer: A

Step-by-step explanation:

1. 49 pic square ft

2. 168 units

3. (4-[tex]\pi[/tex])ft^2

4. 314square ft

5. 22.6 square mm

6. 12 inches

7. 12 [tex]\pi ft^2[/tex]

8. 28.125 [tex]\pi[/tex] square centimeters

9. 22.1 cm

10. (243pi+162) ft^2

Just took the pracitce this will get oyu a 100 hope this helps

the table shows the number of boys and girls that have black, blonde, brown, or red hair color. What is the probability that student is a girl with brown hair? (round to the nearest hundredth)
a. 0.20
b. 0.22
c. 0.40
d. 0.44​

Answers

Answer

The answer is A or 0.20

Step-by-step explanation:

So if you add all the numbers up so (4+4+10+2+5+6+8+1) that would equal=40

8 is the number of girls with brown hair so I would divide 8 by 40

8/40=0.20

Hope this helps!

Answer:

0.20

There are 8 brown-haired girls, out of 40 students.

8

40

which equation best fits these data? PLEASE HELP

Answers

Answer:

C

Step-by-step explanation:

Use a quadratic equation regression calculator.

Plugging in all the points, the equation should come somewhere close to

[tex]y=-0.32x^{2} -1.26x+15.81[/tex]

Which is answer choice C.

Answer:

The correct option is C.

Step-by-step explanation:

Answer:

The required quadratic regression model is [tex]y=x^2-2x-3[/tex].

Step-by-step explanation:

The given data points are (-6,12), (-4,15), (-3,17), (-1,17), (1,15), (2,11), (3,9), (4,6).

From the graph it is clear that the given data forms a U-shaped curve. It means we have to find the quadratic regression model.

The general form of quadratic regression model is

[tex]y=ax^2+bx+c[/tex]

Using technology we get,

[tex]a=-0.32,b=-1.26,c=15.81[/tex]

The required quadratic regression model is

[tex]y=-0.32x^2-1.26x+15.81[/tex]

Therefore the correct option is C.

How long will it take you to ski a distance of 24 miles at a speed of 6 miles per 30 minutes? (Step by step please)

Answers

Answer:

4.8 minutes

Step-by-step explanation:

Time = Speed * Distance

Time = 6 mi / 30 min * 24 miles=  1 mi / 5 min * 24 miles = 0,2 mi / min * 24 = 4.8 minutes

Answer:

So if you know that you can complete 6 miles over the course of 30 minutes it is just matter of multipling 30 minutes times 4, this is becasue it takes 4 times your base distance and time to get to yur goal of 24 miles.

30 x 4 equal 120

which you divide by 60 (because you have 60 minutes in one hour)

so it is safe to say that it will take 2 hours of 120 minutes to ski a ditance of 24 miles at a speed of 6 miles per 30 minutes.

Hope this helps!

Using Cramer’s Rule, what is the value of x in the system of linear equations below?

Answers

Answer:

The answer is the 1st [tex]\frac{\left[\begin{array}{cc}16&3\\8&1\end{array}\right]}{-8}=1[/tex]

Step-by-step explanation:

Lets revise the Cramer's rule

- If the system of equation is ax + by = c and dx + ey = f

- A is the matrix represent this system of equation

- The first column has the coefficients of x, and

  the second column has the coefficients of y

∴ A = [tex]\left[\begin{array}{cc}a&b\\d&e\end{array}\right][/tex]

- Ax means replace the column of x by the answers of the equation

∴ Ax = [tex]\left[\begin{array}{ccc}c&b\\f&e\end{array}\right][/tex]

- Ay means replace the column of y by the answers of the equation

∴ Ay = [tex]\left[\begin{array}{ccc}a&c\\d&f\end{array}\right][/tex]

- x = Dx/D, where Dx is the determinant of Ax and D is the determinant

 of A

- The determinant of A = ae - bd

- The determinant of Ax = ce - bf

* Now lets solve the problem

∵ x + 3y = 16 and 3x + y = 8

∴ A = [tex]\left[\begin{array}{cc}1&3\\3&1\end{array}\right][/tex]

- Replace the column of x by the answer to get Ax

∴ Ax = [tex]\left[\begin{array}{cc}16&3\\8&1\end{array}\right][/tex]

∵ [tex]x=\frac{Dx}{D}[/tex]

∵ Dx = [tex]\left[\begin{array}{cc}16&3\\8&1\end{array}\right]=(16)(1)-(3)(8)=16-24=-8[/tex]

∵ D = [tex]\left[\begin{array}{cc}1&3\\3&1\end{array}\right]=(1)(1)-(3)(3)=1-9=-8[/tex]

∴ x = [tex]\frac{\left[\begin{array}{cc}16&3\\8&1\end{array}\right]}{-8}=\frac{-8}{-8}=1[/tex]

* x = [tex]\frac{\left[\begin{array}{cc}16&3\\8&1\end{array}\right]}{-8}=1[/tex]

First-year students at a school must choose one each of 5 English classes, 4 history classes, 5 math classes, and 3 physical education classes. Find the total number of outcomes

Answers

Answer: 68 total outcomes

                     

Final answer:

To find the total number of outcomes, we multiply the number of options for each class type using the fundamental counting principle, resulting in 5 × 4 × 5 × 3 = 300 total outcomes.

Explanation:

The question asks us to find the total number of outcomes for first-year students at a school who must choose one each of 5 English classes, 4 history classes, 5 math classes, and 3 physical education classes. To calculate the total number of outcomes, we use the fundamental counting principle, which states that if there are m ways to do one thing, and n ways to do another, then there are m × n ways of doing both.

In this scenario, the student can choose:

5 English classes

4 history classes

5 math classes

3 physical education classes

Applying the fundamental counting principle, we multiply the number of options for each subject:

5 (English) × 4 (History) × 5 (Math) × 3 (Physical Education) = 300 total outcomes.

Solve the system of equations.

-5y + 8x = -18

5y + 2x = 58

X = ?
Y= ?

Answers

Answer:

x=4 y=10

Step-by-step explanation:

-5y+8x=-18

5y+2x=58

so the first thing you do is cancel out the 5s then you add the 8+2 and -18+58 then you have 10x=40 then you divide both sides by ten. then you plug that four back into an equation so i did 5y+2(4)=58 then 5y+8=58 you subtract 8 from both sides and you have 5y=50 divide both sides by 5 and you get y=10 and that is how you do that

Which statement represents the transitive property of equality?

Answers

The transitive property of equality is correctly represented by option A, stating that if WX = XY and XY = YZ, then WX = YZ.

The correct answer is option A.

The transitive property of equality states that if two quantities are equal to a third quantity, then they are equal to each other. Among the given options, the statement that represents the transitive property is:

A) If WX = XY and XY = YZ, then WX = YZ.

This statement adheres to the transitive property because it asserts that if WX is equal to XY and XY is equal to YZ, then it logically follows that WX must be equal to YZ. This principle is fundamental in mathematics and logic, providing a way to establish equality relationships through a chain of equalities.

On the other hand, options B and C do not correctly represent the transitive property:

Option B is a statement about the equality of angles, and it does not involve the transitive relationship between two quantities.

Option C represents the reflexive property (an equality is always equal to itself) rather than the transitive property.

In conclusion, option A accurately represents the transitive property of equality.

The question probable may be:

Which statement represents the transitive property of equality?

A) If WX = XY and XY = YZ, then WX = YZ

B) If mZA = mZB, then mZB = mZA

C) If WX = XY, then XY = WX

square root of 6889 with work

Answers

Answer:

83

Step-by-step explanation:

Find center and radius
(x-3)^2+y^2=8

Answers

Answer:

Center: (3, 0)Radius: 2√2

Step-by-step explanation:

The equation of a circle in standard form:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

(h, k) - center

r - radius

We have the equation:

[tex](x-3)^2+y^2=8\to(x-3)^2+(y-0)^2=(\sqrt8)^2[/tex]

Therefore

the center: [tex](3,\ 0)[/tex]

the radius: [tex]r=\sqrt8\to r=\sqrt{4\cdot2}\to r=\sqrt4\cdot\sqrt2\to r=2\sqrt2[/tex]

Stare the various transformations. Help needed !!!

Answers

Answer:

Step-by-step explanation:

Let's start by simplifying a little:

g(x) = -2[(x − 1)² + 3]

g(x) = -2(x − 1)² - 6

The negative sign in front means a reflection about the x axis.  The 2 coefficient means a vertical stretch by a factor of 2.  The x−1 means a horizontal shift to the right by 1 unit.  And the -6 means a vertical shift down six units.

So the answer is the third one.

simplify-3x +2y + x -5x​

Answers

Answer:

3x+2y

Step-by-step explanation:

-3x+2y+x-5x

-5x-3x=-8x+x=-7x

-7x+2y

Answer: [tex]-7x+2y[/tex]

Step-by-step explanation:

You have the expression [tex]-3x +2y + x -5x[/tex]

You can observe that this expresssion has two variables. These are:

"x" and "y"

Then, to simplify the expression given, you need to add the like terms (terms that have the same variable), which are:

[tex]-3x[/tex], [tex]-5x[/tex] and [tex]x[/tex]

Therefore, adding the like terms, you get:

[tex](-3x+x-5x)+2y\\-7x+2y[/tex]

Then, the simplified form of  [tex]-3x +2y + x -5x[/tex] is:

[tex]-7x+2y[/tex]

Help Me Please ! This is so confusing .‍♀️

Answers

Answer: -4

Step-by-step explanation:

3-9=-6

-6*5=-30

-30-1=-31

6*-31=-186

-186+2=-184

8-2=6

6*7=42

42+4=46.

-184/46=-4

Answer and Step-by-step explanation:

All you have to do is follow the order of operations.

We do everything in the first set of parenthesis, then we work our way out.

[tex]\frac{6(5(3-9)-1) + 2}{7(8-2)+4}[/tex]

First, we would subtract 9 from 3, and 2 from 8.

3 - 9 equals -6

8 - 2 equals 6

[tex]\frac{6(5(-6)-1) + 2}{7(6)+4}[/tex]

Now, we multiply those numbers.

5 times -6 equals -30

7 times 6 is 42

[tex]\frac{6(-30 -1) + 2}{42+4}[/tex]

Now, we simplify.

-30 minus 1 equals -31

42 + 4 equals 46

[tex]\frac{6(-31) + 2}{46}[/tex]

Multiply -31 by 6, then add 2 to the product.

-31 times 6 equals -186

-186 plus 2 equals -184

[tex]\frac{-184}{46}[/tex]

Finally, we divide.

-184 divided by 46 equals

-4

-4 is the answer to the expression.

I hope this helps!

#teamtrees #PAW (Plant And Water)

Three more than twice the sum of a number and half the number equals 105. Which equation models this relationship?
A 2(x+1/2x)+3=105
B 2x+1/2x+3=105
C 2x+3=1/2x+105
D 2(x+3)=1/2x+105

Answers

it's a.

three more is +3 and it equals 105

that already eliminates c and d

next it says twice the sum of a number and half the number

Answer:

a

Step-by-step explanation:

A cylindrical container has a radius of 4 inches and a height of 7 inches. to the nearest tenth, what is the volume of the container?

Answers

Answer:351.9

Step-by-step explanation:351.9 cm3

V = πr2h

V = π(4)2(7)

V = π(16)(7)

V = 112π

V = 351.858

Final answer:

The volume of the cylindrical container is approximately 352.6 cubic inches.

Explanation:

To find the volume of a cylindrical container, you can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height. In this case, the radius is 4 inches and the height is 7 inches. Plug these values into the formula:

V = 3.14 x (4 inches)² x 7 inches = 3.14 x 16 square inches x 7 inches = 352.64 cubic inches.

Since the question asks for the volume rounded to the nearest tenth, the answer is approximately 352.6 cubic inches.

Is -2 +-2 A. Positive B. Negative C Both or D None of the above​

Answers

Answer:

B

Step-by-step explanation:

If I have two dollars of debt (negative) and add 2 more dollars of debt (negative), I now owe 4 dollars in debt (negative).

-2+-2=-4

Answer:

B.) Negative 4

Step-by-step explanation:

A negative plus a negative equales a negative, beacause you aren't adding a positive to cancle out some of the numbers. your just adding more negative.

PLEASE HELP!!!
SOLVE FOR X ASAP

Answers

Answer:38

Step-by-step explanation:

Answer:

x = 1

Step-by-step explanation:

Since the triangle is right use Pythagoras' identity to solve for x

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

The hypotenuse is the side opposite the right angle, thus

x² + 1² = ([tex]\sqrt{2}[/tex])²

x² + 1 = 2 ( subtract 1 from both sides )

x² = 1 ( take the square root of both sides )

x = [tex]\sqrt{1}[/tex] = 1

Other Questions
Using the image below, please match the correct trigonometric function with the correct value.sin () =csc() =tan() =sec() =cos() =cot()=Options:1. 8/172. 15/173. 8/154. 15/85. 17/156. 17/8 Who secured an agreement to bring Americans to settle in Texas? Which value of a would make the following expression completely factored x^2-aA)12B)36C)49D)81 13.If you could make recommendations for future healthcare reform, what would your recommendations be and why? Strong evidence that two continents were once joined might include somthe current location of rivers empting into the ocean.A) The current location of rivers emptying into the ocean. b) similar coastal rock formations.c)similar plants growing on the continents today.d) the locations of earthquakes and volcanoes. You purchase 5 pounds of apples and 2 pounds of oranges for $9.Your friend purchases 5 pounds of apples and 6 pounds of oranges for $17. Write and solve a system of linear equations that represents this situation 45 POINTS FOR WHOLE PAGE!!!!!!!!!!!!! If f(x)=|x| + 9 and g(x) =-6 , which describes the value of (f+g)(x) The speed of a tennis ball that is served is 73.14 m/s. During a serve, the ball typically starts from rest and is in contact with the tennis racquet for 30 milliseconds. Assuming constant acceleration, what is the average force exerted on the tennis ball during the serve, expressed in terms of the balls weight w? 450w 150w 250w 350w Whats the process In witch alcohol enters the blood stream and travels to all body parts What is the square root of 36. Please help Sandra has a cylindrical mold for making candles with a radius of 3.4 cm and a height of 6 cm. If Sandra uses a rectangular block of wax measuring 15 cm by 12 cm by 18 cm, about how many candles can she make after melting the block of wax? Easy and Fun Math review questions.Use Pascals triangle to expand each binomial. (a+b)^5 Why does the author use the words "ghostly hollow" and "woody skeleton" to describe the yucca tree (line 6)? To communicate the plant's extraordinary beauty To emphasize the danger of the plant's leaves To highlight the plant's frightening appearance To reveal the author's preoccupation with death Tai notices that although his little brother is not growing by the same amount each month, there is a pattern in how quickly he is growing. Tai determines that each month his brother grows more than he grew the previous month. What type of function could represent Tai's brother's growth? Select one: A. A linear function, because linear functions increase at a constant rate B. A linear function, because linear functions increase at a nonconstant rate C. An exponential function, because exponential functions increase at a constant rate D. An exponential function, because exponential functions increase at a nonconstant rate Read the passage from Cruel Tribute.Years passed by. Every spring when the roses began to bloom seven youths and seven maidens were put on board of a black-sailed ship and sent to Crete to pay the tribute which King Minos required. In every house in Athens there was sorrow and dread, and the people lifted up their hands to Athena on the hilltop and cried out, "How long, O Queen of the Air, how long shall this thing be?"In the meanwhile the little child at Troezen on the other side of the sea had grown to be a man. His name, Theseus, was in everybody's mouth, for he had done great deeds of daring; and at last he had come to Athens to find his father, King Aegeus, who had never heard whether he was alive or dead; and when the youth had made himself known, the king had welcomed him to his home and all the people were glad because so noble a prince had come to dwell among them and, in time, to rule over their city.In this excerpt, the sequence of events creates suspense bystarting the story in the middle of things.describing a setting that causes anticipation.slowing down the plot to focus on an important character.speeding up the plot to move the story forward and build tension. I go further, and affirm that bills of rights, in the sense and to the extent in which they are contended for, are not only unnecessary in the proposed Constitution, but would even be dangerous. Alexander Hamilton, the Federalist Paper 84What point is Alexander Hamilton making? Vicki gives her children dessert 30% of the time. If her children want to know the probability that they will eat dessert 3 of the 7 days this week, which simulation design has an appropriate device and a correct trial?A)Roll a die letting 1 represent eating dessert and 2-6 represent not eating dessert. Roll the die three times.B)Roll a die letting 1 represent eating dessert and 2-6 represent not eating dessert. Roll the die seven times.C)Using a table of random digits select a digit between 0 and 9. Let 0-2 represent eating dessert and 3-9 represent not eating dessert. Select three digits.D)Using a table of random digits select a digit between 0 and 9. Let 0-2 represent eating dessert and 3-9 represent not eating dessert. Select seven digits. Which is the equation of the given line in point- slope form? y - 0 = 1(x+8) y - 0 = -1(x-8)y = - x + 8 y - 8 = -1(x+0) To find 8342 , use the logarithmic equation: log 4,171 log8342log 8,342 - log 1/21/2log8,342